/usr/bin/diffoscope --timeout 7200 --html /srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/statsmodels_0.14.4+dfsg-1.diffoscope.html --text /srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/statsmodels_0.14.4+dfsg-1.diffoscope.txt --json /srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/statsmodels_0.14.4+dfsg-1.diffoscope.json --profile=- /srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/b1/statsmodels_0.14.4+dfsg-1_i386.changes /srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/b2/statsmodels_0.14.4+dfsg-1

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/srv/reproducible-results/rbuild-debian/r-b-build.iiadoTAT/b2/statsmodels_0.14.4+dfsg-1_i386.changes ¶

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python-statsmodels-doc_0.14.4+dfsg-1_all.deb ¶

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control.tar.xz ¶

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control.tar ¶

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./md5sums ¶

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data.tar ¶

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1	·2~~4313bb9d2828~~1~~695e89~~7~~f98~~c~~e90a261~~·396~~58576~~·doc·optional·python-statsmodels-doc_0.14.4+dfsg-1_all.deb	1	·69a4cf65f0be17a49027c6ccc3350847·39661120·doc·optional·python-statsmodels-doc_0.14.4+dfsg-1_all.deb
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1	-rw-r--r--···0········0········0········4·2024-10-05·10:43:25.000000·debian-binary	1	-rw-r--r--···0········0········0········4·2024-10-05·10:43:25.000000·debian-binary
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1	Package:·python-statsmodels-doc	1	Package:·python-statsmodels-doc
2	Source:·statsmodels	2	Source:·statsmodels
3	Version:·0.14.4+dfsg-1	3	Version:·0.14.4+dfsg-1
4	Architecture:·all	4	Architecture:·all
5	Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>	5	Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>
6	Installed-Size:·156090	6	Installed-Size:·156091
7	Depends:·libjs-sphinxdoc·(>=·7.4),·libjs-requirejs,·libjs-mathjax	7	Depends:·libjs-sphinxdoc·(>=·7.4),·libjs-requirejs,·libjs-mathjax
8	Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc	8	Suggests:·python3-statsmodels,·python3-doc,·python-numpy-doc,·python-patsy-doc,·python-pandas-doc,·python-scipy-doc
9	Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)	9	Breaks:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)
10	Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)	10	Replaces:·python-scikits-statsmodels-doc,·python-scikits.statsmodels-doc,·python-statsmodels·(<<·0.9.0-3~)
11	Section:·doc	11	Section:·doc
12	Priority:·optional	12	Priority:·optional
13	Homepage:·https://www.statsmodels.org	13	Homepage:·https://www.statsmodels.org


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32	············"source":·[	32	············"source":·[
Offset 39, 18 lines modified		Offset 39, 18 lines modified
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41	········{	41	········{
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44	············"metadata":·{	44	············"metadata":·{
45	················"execution":·{	45	················"execution":·{
46	····················"iopub.execute_input":·"2025-12-11T02:55:35.~~013622~~Z",	46	····················"iopub.execute_input":·"2024-11-07T21:30:25.291037Z",
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55	············"outputs":·[],	55	············"outputs":·[],
56	············"source":·[	56	············"source":·[
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63	········{	63	········{
64	············"cell_type":·"code",	64	············"cell_type":·"code",
65	············"execution_count":·3,	65	············"execution_count":·3,
66	············"metadata":·{	66	············"metadata":·{
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-11T02:55:35.020549Z",	68	····················"iopub.execute_input":·"2024-11-07T21:30:25.302640Z",
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75	················}	75	················}
76	············},	76	············},
77	············"outputs":·[	77	············"outputs":·[
78	················{	78	················{


Offset 120, 15 lines modified		Offset 120, 15 lines modified
120	</div>	120	</div>
121	</div>	121	</div>
122	<div·class="nboutput·docutils·container">	122	<div·class="nboutput·docutils·container">
123	<div·class="prompt·empty·docutils·container">	123	<div·class="prompt·empty·docutils·container">
124	</div>	124	</div>
125	<div·class="output_area·stderr·docutils·container">	125	<div·class="output_area·stderr·docutils·container">
126	<div·class="highlight"><pre>	126	<div·class="highlight"><pre>
127	/tmp/ipykernel_1321/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\s+'``·instead	127	/tmp/ipykernel_10219/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\s+'``·instead
128	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	128	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)
129	</pre></div></div>	129	</pre></div></div>
130	</div>	130	</div>
131	<div·class="nboutput·nblast·docutils·container">	131	<div·class="nboutput·nblast·docutils·container">
132	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:	132	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:
133	</pre></div>	133	</pre></div>
134	</div>	134	</div>


Offset 56, 15 lines modified		Offset 56, 15 lines modified
56	except·ImportError:	56	except·ImportError:
57	····from·io·import·StringIO	57	····from·io·import·StringIO
58	data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	58	data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)

59	#·Note:·for·the·results·we·compare·with·the·paper·here,·they·drop·the·first	59	#·Note:·for·the·results·we·compare·with·the·paper·here,·they·drop·the·first
60	four·points	60	four·points
61	data.head()	61	data.head()
62	/tmp/ipykernel_1321/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'	62	/tmp/ipykernel_10219/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'
63	keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.	63	keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.
64	Use·``sep='\s+'``·instead	64	Use·``sep='\s+'``·instead
65	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)	65	··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)
66	[2]:	66	[2]:
67	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·	67	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·
68	\|_\x8·_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8x\x8x_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8y\x8y_\x8\|_\x8y\x8y_\x8_\x8__\x8e\x8e_\x8r\x8r_\x8r\x8r\|	68	\|_\x8·_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8x\x8x_\x8\|_\x8·_\x8·_\x8·_\x8·_\x8y\x8y_\x8\|_\x8y\x8y_\x8_\x8__\x8e\x8e_\x8r\x8r_\x8r\x8r\|
69	\|_\x80\x80_\x8\|_\x82_\x80_\x81_\x8._\x80_\x8\|_\x85_\x89_\x82_\x8._\x80_\x8\|_\x86_\x81_\x8._\x80_\x8·\|	69	\|_\x80\x80_\x8\|_\x82_\x80_\x81_\x8._\x80_\x8\|_\x85_\x89_\x82_\x8._\x80_\x8\|_\x86_\x81_\x8._\x80_\x8·\|


Offset 19, 18 lines modified		Offset 19, 18 lines modified
19	············]	19	············]
20	········},	20	········},
21	········{	21	········{
22	············"cell_type":·"code",	22	············"cell_type":·"code",
23	············"execution_count":·1,	23	············"execution_count":·1,
24	············"metadata":·{	24	············"metadata":·{
25	················"execution":·{	25	················"execution":·{
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29	····················"shell.execute_reply":·"2025-12-11T02:56:04.673~~676~~Z"	29	····················"shell.execute_reply":·"2024-11-07T21:29:31.367501Z"
30	················},	30	················},
31	················"jupyter":·{	31	················"jupyter":·{
32	····················"outputs_hidden":·false	32	····················"outputs_hidden":·false
33	················}	33	················}
34	············},	34	············},
35	············"outputs":·[],	35	············"outputs":·[],
36	············"source":·[	36	············"source":·[
Offset 62, 29 lines modified		Offset 62, 29 lines modified
62	············]	62	············]
63	········},	63	········},
64	········{	64	········{
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67	············"metadata":·{	67	············"metadata":·{
68	················"execution":·{	68	················"execution":·{
69	····················"iopub.execute_input":·"2025-12-11T02:56:04.677104Z",	69	····················"iopub.execute_input":·"2024-11-07T21:29:31.371134Z",
70	····················"iopub.status.busy":·"2025-12-11T02:56:04.67~~678~~6Z",	70	····················"iopub.status.busy":·"2024-11-07T21:29:31.370866Z",
71	····················"iopub.status.idle":·"2025-12-11T02:56:04.~~692341~~Z",	71	····················"iopub.status.idle":·"2024-11-07T21:29:31.415967Z",
72	····················"shell.execute_reply":·"2025-12-11T02:56:04.~~69192~~1Z"	72	····················"shell.execute_reply":·"2024-11-07T21:29:31.415501Z"
73	················},	73	················},
74	················"jupyter":·{	74	················"jupyter":·{
75	····················"outputs_hidden":·false	75	····················"outputs_hidden":·false
76	················}	76	················}
77	············},	77	············},
78	············"outputs":·[	78	············"outputs":·[
79	················{	79	················{
80	····················"name":·"stderr",	80	····················"name":·"stderr",
81	····················"output_type":·"stream",	81	····················"output_type":·"stream",
82	····················"text":·[	82	····················"text":·[
83	························"/tmp/ipykernel_1321/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\\s+'``·instead\n",	83	························"/tmp/ipykernel_10219/2751177292.py:28:·FutureWarning:·The·'delim_whitespace'·keyword·in·pd.read_csv·is·deprecated·and·will·be·removed·in·a·future·version.·Use·``sep='\\s+'``·instead\n",
84	························"··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)\n"	84	························"··data·=·pd.read_csv(StringIO(data),·delim_whitespace=True).astype(float)\n"
85	····················]	85	····················]
86	················},	86	················},
87	················{	87	················{
88	····················"data":·{	88	····················"data":·{
89	························"text/html":·[	89	························"text/html":·[
90	····························"<div>\n",	90	····························"<div>\n",
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213	············"metadata":·{	213	············"metadata":·{
214	················"execution":·{	214	················"execution":·{
215	····················"iopub.execute_input":·"2025-12-11T02:56:04.~~699~~852Z",	215	····················"iopub.execute_input":·"2024-11-07T21:29:31.418852Z",
216	····················"iopub.status.busy":·"2025-12-11T02:56:04.~~6994~~97Z",	216	····················"iopub.status.busy":·"2024-11-07T21:29:31.418599Z",
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218	····················"shell.execute_reply":·"2025-12-11T02:56:04.~~723158~~Z"	218	····················"shell.execute_reply":·"2024-11-07T21:29:31.467503Z"
219	················},	219	················},
220	················"jupyter":·{	220	················"jupyter":·{
221	····················"outputs_hidden":·false	221	····················"outputs_hidden":·false
222	················}	222	················}
223	············},	223	············},
224	············"outputs":·[	224	············"outputs":·[
225	················{	225	················{
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276	············"metadata":·{	276	············"metadata":·{
277	················"execution":·{	277	················"execution":·{
278	····················"iopub.execute_input":·"2025-12-11T02:56:04.~~726406~~Z",	278	····················"iopub.execute_input":·"2024-11-07T21:29:31.471022Z",
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286	············},	286	············},
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288	················{	288	················{
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372	············]	372	············]
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89	········},	89	········},
90	········{	90	········{
91	············"cell_type":·"code",	91	············"cell_type":·"code",
92	············"execution_count":·4,	92	············"execution_count":·4,
93	············"metadata":·{	93	············"metadata":·{
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2025-12-11T02:55:41.204257Z",	95	····················"iopub.execute_input":·"2024-11-07T21:29:01.290490Z",
96	····················"iopub.status.busy":·"2025-12-11T02:55:41.204080Z",	96	····················"iopub.status.busy":·"2024-11-07T21:29:01.290303Z",
97	····················"iopub.status.idle":·"2025-12-11T02:55:41.20~~7410~~Z",	97	····················"iopub.status.idle":·"2024-11-07T21:29:01.303949Z",
98	····················"shell.execute_reply":·"2025-12-11T02:55:41.20~~7023~~Z"	98	····················"shell.execute_reply":·"2024-11-07T21:29:01.303484Z"
99	················}	99	················}
100	············},	100	············},
101	············"outputs":·[	101	············"outputs":·[
102	················{	102	················{
103	····················"name":·"stdout",	103	····················"name":·"stdout",
104	····················"output_type":·"stream",	104	····················"output_type":·"stream",
105	····················"text":·[	105	····················"text":·[
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140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
143	············"execution_count":·5,	143	············"execution_count":·5,
144	············"metadata":·{	144	············"metadata":·{
145	················"execution":·{	145	················"execution":·{
146	····················"iopub.execute_input":·"2025-12-11T02:55:41.209508Z",	146	····················"iopub.execute_input":·"2024-11-07T21:29:01.306502Z",
147	····················"iopub.status.busy":·"2025-12-11T02:55:41.209213Z",	147	····················"iopub.status.busy":·"2024-11-07T21:29:01.306314Z",
148	····················"iopub.status.idle":·"2025-12-11T02:55:41.23~~032~~6Z",	148	····················"iopub.status.idle":·"2024-11-07T21:29:01.336016Z",
149	····················"shell.execute_reply":·"2025-12-11T02:55:41.~~229639~~Z"	149	····················"shell.execute_reply":·"2024-11-07T21:29:01.335511Z"
150	················}	150	················}
151	············},	151	············},
152	············"outputs":·[],	152	············"outputs":·[],
153	············"source":·[	153	············"source":·[
154	················"dta·=·sm.datasets.fair.load_pandas().data"	154	················"dta·=·sm.datasets.fair.load_pandas().data"
155	············]	155	············]
156	········},	156	········},
157	········{	157	········{
158	············"cell_type":·"code",	158	············"cell_type":·"code",
159	············"execution_count":·6,	159	············"execution_count":·6,
160	············"metadata":·{	160	············"metadata":·{
161	················"execution":·{	161	················"execution":·{
162	····················"iopub.execute_input":·"2025-12-11T02:55:41.233527Z",	162	····················"iopub.execute_input":·"2024-11-07T21:29:01.338775Z",
163	····················"iopub.status.busy":·"2025-12-11T02:55:41.23~~3099~~Z",	163	····················"iopub.status.busy":·"2024-11-07T21:29:01.338553Z",
164	····················"iopub.status.idle":·"2025-12-11T02:55:41.~~254212~~Z",	164	····················"iopub.status.idle":·"2024-11-07T21:29:01.372045Z",
165	····················"shell.execute_reply":·"2025-12-11T02:55:41.~~253636~~Z"	165	····················"shell.execute_reply":·"2024-11-07T21:29:01.371507Z"
166	················}	166	················}
167	············},	167	············},
168	············"outputs":·[	168	············"outputs":·[
169	················{	169	················{
170	····················"name":·"stdout",	170	····················"name":·"stdout",
171	····················"output_type":·"stream",	171	····················"output_type":·"stream",
172	····················"text":·[	172	····················"text":·[
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203	········},	203	········},
204	········{	204	········{
205	············"cell_type":·"code",	205	············"cell_type":·"code",
206	············"execution_count":·7,	206	············"execution_count":·7,
207	············"metadata":·{	207	············"metadata":·{
208	················"execution":·{	208	················"execution":·{
209	····················"iopub.execute_input":·"2025-12-11T02:55:41.~~25667~~3Z",	209	····················"iopub.execute_input":·"2024-11-07T21:29:01.374823Z",
210	····················"iopub.status.busy":·"2025-12-11T02:55:41.256491Z",	210	····················"iopub.status.busy":·"2024-11-07T21:29:01.374619Z",
211	····················"iopub.status.idle":·"2025-12-11T02:55:41.~~287351~~Z",	211	····················"iopub.status.idle":·"2024-11-07T21:29:01.452038Z",
212	····················"shell.execute_reply":·"2025-12-11T02:55:41.~~286933~~Z"	212	····················"shell.execute_reply":·"2024-11-07T21:29:01.451491Z"
213	················}	213	················}
214	············},	214	············},
215	············"outputs":·[	215	············"outputs":·[
216	················{	216	················{
217	····················"name":·"stdout",	217	····················"name":·"stdout",
218	····················"output_type":·"stream",	218	····················"output_type":·"stream",
219	····················"text":·[	219	····················"text":·[
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12	········{	12	········{
13	············"cell_type":·"code",	13	············"cell_type":·"code",
14	············"execution_count":·1,	14	············"execution_count":·1,
15	············"metadata":·{	15	············"metadata":·{
16	················"execution":·{	16	················"execution":·{
17	····················"iopub.execute_input":·"2025-12-11T02:55:09.239770Z",	17	····················"iopub.execute_input":·"2024-11-07T21:29:35.497264Z",
18	····················"iopub.status.busy":·"2025-12-11T02:55:09.~~239475~~Z",	18	····················"iopub.status.busy":·"2024-11-07T21:29:35.496898Z",
19	····················"iopub.status.idle":·"2025-12-11T02:55:09.846093Z",	19	····················"iopub.status.idle":·"2024-11-07T21:29:37.304179Z",
20	····················"shell.execute_reply":·"2025-12-11T02:55:09.~~845630~~Z"	20	····················"shell.execute_reply":·"2024-11-07T21:29:37.303511Z"
21	················}	21	················}
22	············},	22	············},
23	············"outputs":·[],	23	············"outputs":·[],
24	············"source":·[	24	············"source":·[
25	················"import·numpy·as·np\n",	25	················"import·numpy·as·np\n",
26	················"from·scipy.stats.distributions·import·norm\n",	26	················"from·scipy.stats.distributions·import·norm\n",
27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",	27	················"from·statsmodels.base.distributed_estimation·import·DistributedModel\n",
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61	············]	61	············]
62	········},	62	········},
63	········{	63	········{
64	············"cell_type":·"code",	64	············"cell_type":·"code",
65	············"execution_count":·2,	65	············"execution_count":·2,
66	············"metadata":·{	66	············"metadata":·{
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-11T02:55:09.850132Z",	68	····················"iopub.execute_input":·"2024-11-07T21:29:37.310842Z",
69	····················"iopub.status.busy":·"2025-12-11T02:55:09.~~849903~~Z",	69	····················"iopub.status.busy":·"2024-11-07T21:29:37.310520Z",
70	····················"iopub.status.idle":·"2025-12-11T02:55:09.~~890749~~Z",	70	····················"iopub.status.idle":·"2024-11-07T21:29:37.328128Z",
71	····················"shell.execute_reply":·"2025-12-11T02:55:09.~~89031~~6Z"	71	····················"shell.execute_reply":·"2024-11-07T21:29:37.327526Z"
72	················}	72	················}
73	············},	73	············},
74	············"outputs":·[],	74	············"outputs":·[],
75	············"source":·[	75	············"source":·[
76	················"X·=·np.random.normal(size=(1000,·25))\n",	76	················"X·=·np.random.normal(size=(1000,·25))\n",
77	················"beta·=·np.random.normal(size=25)\n",	77	················"beta·=·np.random.normal(size=25)\n",
78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",	78	················"beta·*=·np.random.randint(0,·2,·size=25)\n",
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88	············]	88	············]
89	········},	89	········},
90	········{	90	········{
91	············"cell_type":·"code",	91	············"cell_type":·"code",
92	············"execution_count":·3,	92	············"execution_count":·3,
93	············"metadata":·{	93	············"metadata":·{
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2025-12-11T02:55:09.~~898785~~Z",	95	····················"iopub.execute_input":·"2024-11-07T21:29:37.331824Z",
96	····················"iopub.status.busy":·"2025-12-11T02:55:09.~~898443~~Z",	96	····················"iopub.status.busy":·"2024-11-07T21:29:37.331582Z",
97	····················"iopub.status.idle":·"2025-12-11T02:55:10.~~2261~~09Z",	97	····················"iopub.status.idle":·"2024-11-07T21:29:37.681405Z",
98	····················"shell.execute_reply":·"2025-12-11T02:55:10.~~225636~~Z"	98	····················"shell.execute_reply":·"2024-11-07T21:29:37.680170Z"
99	················}	99	················}
100	············},	100	············},
101	············"outputs":·[],	101	············"outputs":·[],
102	············"source":·[	102	············"source":·[
103	················"debiased_OLS_mod·=·DistributedModel(m)\n",	103	················"debiased_OLS_mod·=·DistributedModel(m)\n",
104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",	104	················"debiased_OLS_fit·=·debiased_OLS_mod.fit(\n",
105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",	105	················"····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={\"alpha\":·0.2}\n",
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114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·4,	118	············"execution_count":·4,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2025-12-11T02:55:10.~~230725~~Z",	121	····················"iopub.execute_input":·"2024-11-07T21:29:37.684866Z",
122	····················"iopub.status.busy":·"2025-12-11T02:55:10.~~230461~~Z",	122	····················"iopub.status.busy":·"2024-11-07T21:29:37.684536Z",
123	····················"iopub.status.idle":·"2025-12-11T02:55:10.478~~185~~Z",	123	····················"iopub.status.idle":·"2024-11-07T21:29:38.368057Z",
124	····················"shell.execute_reply":·"2025-12-11T02:55:10.477~~660~~Z"	124	····················"shell.execute_reply":·"2024-11-07T21:29:38.367508Z"
125	················}	125	················}
126	············},	126	············},
127	············"outputs":·[],	127	············"outputs":·[],
128	············"source":·[	128	············"source":·[
129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",	129	················"from·statsmodels.genmod.generalized_linear_model·import·GLM\n",
130	················"from·statsmodels.genmod.families·import·Gaussian\n",	130	················"from·statsmodels.genmod.families·import·Gaussian\n",
131	················"\n",	131	················"\n",
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145	············]	145	············]
146	········},	146	········},
147	········{	147	········{
148	············"cell_type":·"code",	148	············"cell_type":·"code",
149	············"execution_count":·5,	149	············"execution_count":·5,
150	············"metadata":·{	150	············"metadata":·{
151	················"execution":·{	151	················"execution":·{
152	····················"iopub.execute_input":·"2025-12-11T02:55:10.~~483~~971Z",	152	····················"iopub.execute_input":·"2024-11-07T21:29:38.370999Z",
153	····················"iopub.status.busy":·"2025-12-11T02:55:10.~~483803~~Z",	153	····················"iopub.status.busy":·"2024-11-07T21:29:38.370797Z",
154	····················"iopub.status.idle":·"2025-12-11T02:55:10.~~558~~142Z",	154	····················"iopub.status.idle":·"2024-11-07T21:29:38.604130Z",
155	····················"shell.execute_reply":·"2025-12-11T02:55:10.~~557650~~Z"	155	····················"shell.execute_reply":·"2024-11-07T21:29:38.603515Z"
156	················}	156	················}
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",	160	················"from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,·_join_naive\n",
161	················"\n",	161	················"\n",
162	················"\n",	162	················"\n",
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176	············]	176	············]
177	········},	177	········},
178	········{	178	········{
179	············"cell_type":·"code",	179	············"cell_type":·"code",
180	············"execution_count":·6,	180	············"execution_count":·6,
181	············"metadata":·{	181	············"metadata":·{
182	················"execution":·{	182	················"execution":·{
183	····················"iopub.execute_input":·"2025-12-11T02:55:10.~~563~~135Z",	183	····················"iopub.execute_input":·"2024-11-07T21:29:38.607106Z",
184	····················"iopub.status.busy":·"2025-12-11T02:55:10.~~562855~~Z",	184	····················"iopub.status.busy":·"2024-11-07T21:29:38.606903Z",
185	····················"iopub.status.idle":·"2025-12-11T02:55:10.~~575348~~Z",	185	····················"iopub.status.idle":·"2024-11-07T21:29:38.648016Z",
186	····················"shell.execute_reply":·"2025-12-11T02:55:10.574968Z"	186	····················"shell.execute_reply":·"2024-11-07T21:29:38.647499Z"
187	················}	187	················}
188	············},	188	············},
189	············"outputs":·[],	189	············"outputs":·[],
190	············"source":·[	190	············"source":·[
191	················"from·statsmodels.base.distributed_estimation·import·(\n",	191	················"from·statsmodels.base.distributed_estimation·import·(\n",
192	················"····_est_unregularized_naive,\n",	192	················"····_est_unregularized_naive,\n",
193	················"····DistributedResults,\n",	193	················"····DistributedResults,\n",


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22	········},	22	········},
23	········{	23	········{
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32	················}	32	················}
33	············},	33	············},
34	············"outputs":·[],	34	············"outputs":·[],
35	············"source":·[	35	············"source":·[
36	················"import·numpy·as·np\n",	36	················"import·numpy·as·np\n",
37	················"import·matplotlib.pyplot·as·plt\n",	37	················"import·matplotlib.pyplot·as·plt\n",
38	················"import·pandas·as·pd\n",	38	················"import·pandas·as·pd\n",
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43	············]	43	············]
44	········},	44	········},
45	········{	45	········{
46	············"cell_type":·"code",	46	············"cell_type":·"code",
47	············"execution_count":·2,	47	············"execution_count":·2,
48	············"metadata":·{	48	············"metadata":·{
49	················"execution":·{	49	················"execution":·{
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54	················}	54	················}
55	············},	55	············},
56	············"outputs":·[],	56	············"outputs":·[],
57	············"source":·[	57	············"source":·[
58	················"plt.rcParams[\"figure.figsize\"]·=·(12,·8)"	58	················"plt.rcParams[\"figure.figsize\"]·=·(12,·8)"
59	············]	59	············]
60	········},	60	········},
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83	········},	83	········},
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93	················}	93	················}
94	············},	94	············},
95	············"outputs":·[	95	············"outputs":·[
96	················{	96	················{
97	····················"data":·{	97	····················"data":·{
98	························"text/plain":·[	98	························"text/plain":·[
99	····························"Text(0,·0.5,·'Annual·oil·production·in·Saudi·Arabia·(Mt)')"	99	····························"Text(0,·0.5,·'Annual·oil·production·in·Saudi·Arabia·(Mt)')"
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180	············]	180	············]
181	········},	181	········},
182	········{	182	········{
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185	············"metadata":·{	185	············"metadata":·{
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191	················}	191	················}
192	············},	192	············},
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194	················{	194	················{
195	····················"name":·"stdout",	195	····················"name":·"stdout",
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296	················}	296	················}
297	············},	297	············},
298	············"outputs":·[	298	············"outputs":·[
299	················{	299	················{
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396	················}	396	················}
397	············},	397	············},
398	············"outputs":·[	398	············"outputs":·[
399	················{	399	················{
400	····················"name":·"stdout",	400	····················"name":·"stdout",
401	····················"output_type":·"stream",	401	····················"output_type":·"stream",
402	····················"text":·[	402	····················"text":·[
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189	</div>	189	</div>
190	</div>	190	</div>
191	<div·class="nboutput·nblast·docutils·container">	191	<div·class="nboutput·nblast·docutils·container">
192	<div·class="prompt·empty·docutils·container">	192	<div·class="prompt·empty·docutils·container">
193	</div>	193	</div>
194	<div·class="output_area·stderr·docutils·container">	194	<div·class="output_area·stderr·docutils·container">
195	<div·class="highlight"><pre>	195	<div·class="highlight"><pre>
196	/tmp/ipykernel_4692/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	196	/tmp/ipykernel_26290/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
197	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")	197	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")
198	/tmp/ipykernel_4692/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	198	/tmp/ipykernel_26290/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
199	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")	199	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")
200	/tmp/ipykernel_4692/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	200	/tmp/ipykernel_26290/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
201	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")	201	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")
202	/tmp/ipykernel_4692/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.	202	/tmp/ipykernel_26290/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'YE'·instead.
203	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")	203	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")
204	</pre></div></div>	204	</pre></div></div>
205	</div>	205	</div>
206	</section>	206	</section>
207	<section·id="Simple-Exponential-Smoothing">	207	<section·id="Simple-Exponential-Smoothing">
208	<h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>	208	<h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>
209	<p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>	209	<p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>


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126	····59.7668,	126	····59.7668,
127	····35.1919,	127	····35.1919,
128	····44.3197,	128	····44.3197,
129	····47.9137,	129	····47.9137,
130	]	130	]
131	index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")	131	index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")
132	aust·=·pd.Series(data,·index)	132	aust·=·pd.Series(data,·index)
133	/tmp/ipykernel_4692/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and~~·will~~	133	/tmp/ipykernel_26290/3508103541.py:24:·FutureWarning:·'Y'·is·deprecated·and
134	be·removed·in·a·future·version,·please·use·'YE'·instead.	134	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
135	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")	135	··index·=·pd.date_range(start="1996",·end="2008",·freq="Y")
136	/tmp/ipykernel_4692/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and~~·will~~	136	/tmp/ipykernel_26290/3508103541.py:44:·FutureWarning:·'Y'·is·deprecated·and
137	be·removed·in·a·future·version,·please·use·'YE'·instead.	137	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
138	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")	138	··index·=·pd.date_range(start="1990",·end="2005",·freq="Y")
139	/tmp/ipykernel_4692/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and~~·will~~	139	/tmp/ipykernel_26290/3508103541.py:80:·FutureWarning:·'Y'·is·deprecated·and
140	be·removed·in·a·future·version,·please·use·'YE'·instead.	140	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
141	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")	141	··index·=·pd.date_range(start="1970",·end="2001",·freq="Y")
142	/tmp/ipykernel_4692/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and~~·will~~	142	/tmp/ipykernel_26290/3508103541.py:84:·FutureWarning:·'Y'·is·deprecated·and
143	be·removed·in·a·future·version,·please·use·'YE'·instead.	143	will·be·removed·in·a·future·version,·please·use·'YE'·instead.
144	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")	144	··index·=·pd.date_range(start="2001",·end="2008",·freq="Y")
145	\x8\x8\x8\x8\x8·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8¶·\x8\x8\x8\x8\x8	145	\x8\x8\x8\x8\x8·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8¶·\x8\x8\x8\x8\x8
146	Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.	146	Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.
147	[2]:	147	[2]:
148	ax·=·oildata.plot()	148	ax·=·oildata.plot()
149	ax.set_xlabel("Year")	149	ax.set_xlabel("Year")
150	ax.set_ylabel("Oil·(millions·of·tonnes)")	150	ax.set_ylabel("Oil·(millions·of·tonnes)")


Offset 230, 27 lines modified		Offset 230, 27 lines modified
230	······<th></th>	230	······<th></th>
231	······<th>Variance</th>	231	······<th>Variance</th>
232	····</tr>	232	····</tr>
233	··</thead>	233	··</thead>
234	··<tbody>	234	··<tbody>
235	····<tr>	235	····<tr>
236	······<th>groups_ix</th>	236	······<th>groups_ix</th>
237	······<td>1.~~064624~~</td>	237	······<td>0.923016</td>
238	····</tr>	238	····</tr>
239	····<tr>	239	····<tr>
240	······<th>level1_ix</th>	240	······<th>level1_ix</th>
241	······<td>2.0~~62466~~</td>	241	······<td>2.096815</td>
242	····</tr>	242	····</tr>
243	····<tr>	243	····<tr>
244	······<th>level2_ix</th>	244	······<th>level2_ix</th>
245	······<td>2.9~~65443~~</td>	245	······<td>2.982774</td>
246	····</tr>	246	····</tr>
247	····<tr>	247	····<tr>
248	······<th>Residual</th>	248	······<th>Residual</th>
249	······<td>4.0~~31346~~</td>	249	······<td>4.012599</td>
250	····</tr>	250	····</tr>
251	··</tbody>	251	··</tbody>
252	</table>	252	</table>
253	</div></div>	253	</div></div>
254	</div>	254	</div>
255	</section>	255	</section>


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79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,	79	The·estimated·covariance·parameters·should·be·similar·to·groups_var,
80	level1_var,·etc.·as·defined·above.	80	level1_var,·etc.·as·defined·above.
81	[13]:	81	[13]:
82	r.cov_struct.summary()	82	r.cov_struct.summary()
83	[13]:	83	[13]:
84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·	84	·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·
85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|	85	\|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8\|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e\|
86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_.._.0_.6_.4_.6_.2_.4\|	86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x80_.._.9_.2_.3_.0_.1_.6\|
		87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x80_\x89_\x86_\x88_\x81_\x85\|
87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81.1_._.__.i.i_.x.x_.\|_.2_.._.0_.6_.2_.4_.6_.6\|	88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82.2_._.__.i.i_.x.x_.\|_.2_.._.9_.8_.2_.7_.7_.4\|
88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x89_\x86_\x85_\x84_\x84_\x83\|
89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x84_\x8._\x80_\x83_.1_.3_.4_.6\|	89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x84_\x8._\x80_\x81_.2_.5_.9_.9\|
90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
91	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	91	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8
92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s	92	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d	93	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
94	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e	94	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
95	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s	95	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s
96	····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e	96	····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e


Offset 449, 14 lines modified		Offset 449, 23 lines modified
449	<span·class="nb">print</span><span·class="p">(</span><span·class="n">mdf</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>	449	<span·class="nb">print</span><span·class="p">(</span><span·class="n">mdf</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
450	</pre></div>	450	</pre></div>
451	</div>	451	</div>
452	</div>	452	</div>
453	<div·class="nboutput·docutils·container">	453	<div·class="nboutput·docutils·container">
454	<div·class="prompt·empty·docutils·container">	454	<div·class="prompt·empty·docutils·container">
455	</div>	455	</div>
		456	<div·class="output_area·stderr·docutils·container">
		457	<div·class="highlight"><pre>
		458	/usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:2237:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter·space.
		459	··warnings.warn(msg,·ConvergenceWarning)
		460	</pre></div></div>
		461	</div>
		462	<div·class="nboutput·nblast·docutils·container">
		463	<div·class="prompt·empty·docutils·container">
		464	</div>
456	<div·class="output_area·docutils·container">	465	<div·class="output_area·docutils·container">
457	<div·class="highlight"><pre>	466	<div·class="highlight"><pre>
458	·············Mixed·Linear·Model·Regression·Results	467	·············Mixed·Linear·Model·Regression·Results
459	===============================================================	468	===============================================================
460	Model:···············MixedLM····Dependent·Variable:····size	469	Model:···············MixedLM····Dependent·Variable:····size
461	No.·Observations:····395········Method:················REML	470	No.·Observations:····395········Method:················REML
462	No.·Groups:··········79·········Scale:·················0.0264	471	No.·Groups:··········79·········Scale:·················0.0264
Offset 471, 23 lines modified		Offset 480, 14 lines modified
471	Intercept·Var·········0.646····0.914	480	Intercept·Var·········0.646····0.914
472	Intercept·x·Time·Cov·-0.001····0.003	481	Intercept·x·Time·Cov·-0.001····0.003
473	Time·Var··············0.000····0.000	482	Time·Var··············0.000····0.000
474	===============================================================	483	===============================================================

475	</pre></div></div>	484	</pre></div></div>
476	</div>	485	</div>
477	<div·class="nboutput·nblast·docutils·container">
478	<div·class="prompt·empty·docutils·container">
479	</div>
480	<div·class="output_area·stderr·docutils·container">
481	<div·class="highlight"><pre>
482	/usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:2237:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter·space.
483	··warnings.warn(msg,·ConvergenceWarning)


Offset 316, 14 lines modified		Offset 316, 18 lines modified
316	being·on·the·boundary·of·the·parameter·space.·The·regression·slopes·agree·very	316	being·on·the·boundary·of·the·parameter·space.·The·regression·slopes·agree·very
317	well·with·R,·but·the·likelihood·value·is·much·higher·than·that·returned·by·R.	317	well·with·R,·but·the·likelihood·value·is·much·higher·than·that·returned·by·R.
318	[8]:	318	[8]:
319	exog_re·=·exog.copy()	319	exog_re·=·exog.copy()
320	md·=·sm.MixedLM(endog,·exog,·data["tree"],·exog_re)	320	md·=·sm.MixedLM(endog,·exog,·data["tree"],·exog_re)
321	mdf·=·md.fit()	321	mdf·=·md.fit()
322	print(mdf.summary())	322	print(mdf.summary())
		323	/usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:
		324	2237:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter
		325	space.
		326	··warnings.warn(msg,·ConvergenceWarning)
323	·············Mixed·Linear·Model·Regression·Results	327	·············Mixed·Linear·Model·Regression·Results
324	===============================================================	328	===============================================================
325	Model:···············MixedLM····Dependent·Variable:····size	329	Model:···············MixedLM····Dependent·Variable:····size
326	No.·Observations:····395········Method:················REML	330	No.·Observations:····395········Method:················REML
327	No.·Groups:··········79·········Scale:·················0.0264	331	No.·Groups:··········79·········Scale:·················0.0264
328	Min.·group·size:·····5··········Log-Likelihood:········-62.4834	332	Min.·group·size:·····5··········Log-Likelihood:········-62.4834
329	Max.·group·size:·····5··········Converged:·············Yes	333	Max.·group·size:·····5··········Converged:·············Yes
Offset 333, 18 lines modified		Offset 337, 14 lines modified
333	---------------------------------------------------------------	337	---------------------------------------------------------------
334	Intercept·············2.273····0.101·22.513·0.000··2.075··2.471	338	Intercept·············2.273····0.101·22.513·0.000··2.075··2.471
335	Time··················0.013····0.000·33.888·0.000··0.012··0.013	339	Time··················0.013····0.000·33.888·0.000··0.012··0.013
336	Intercept·Var·········0.646····0.914	340	Intercept·Var·········0.646····0.914
337	Intercept·x·Time·Cov·-0.001····0.003	341	Intercept·x·Time·Cov·-0.001····0.003
338	Time·Var··············0.000····0.000	342	Time·Var··············0.000····0.000
339	===============================================================	343	===============================================================
340	/usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:
341	2237:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter
342	space.
343	··warnings.warn(msg,·ConvergenceWarning)
344	We·can·further·explore·the·random·effects·structure·by·constructing·plots·of	344	We·can·further·explore·the·random·effects·structure·by·constructing·plots·of
345	the·profile·likelihoods.·We·start·with·the·random·intercept,·generating·a·plot	345	the·profile·likelihoods.·We·start·with·the·random·intercept,·generating·a·plot
346	of·the·profile·likelihood·from·0.1·units·below·to·0.1·units·above·the·MLE.	346	of·the·profile·likelihood·from·0.1·units·below·to·0.1·units·above·the·MLE.
347	Since·each·optimization·inside·the·profile·likelihood·generates·a·warning·(due	347	Since·each·optimization·inside·the·profile·likelihood·generates·a·warning·(due
348	to·the·random·slope·variance·being·close·to·zero),·we·turn·off·the·warnings	348	to·the·random·slope·variance·being·close·to·zero),·we·turn·off·the·warnings
349	here.	349	here.
350	[9]:	350	[9]:


Offset 12, 18 lines modified		Offset 12, 18 lines modified
12	············]	12	············]
13	········},	13	········},
14	········{	14	········{
15	············"cell_type":·"code",	15	············"cell_type":·"code",
16	············"execution_count":·1,	16	············"execution_count":·1,
17	············"metadata":·{	17	············"metadata":·{
18	················"execution":·{	18	················"execution":·{
19	····················"iopub.execute_input":·"2025-12-11T02:55:15.~~291676~~Z",	19	····················"iopub.execute_input":·"2024-11-07T21:30:21.122252Z",
20	····················"iopub.status.busy":·"2025-12-11T02:55:15.~~29150~~2Z",	20	····················"iopub.status.busy":·"2024-11-07T21:30:21.122012Z",
21	····················"iopub.status.idle":·"2025-12-11T02:55:16.~~338824~~Z",	21	····················"iopub.status.idle":·"2024-11-07T21:30:22.744037Z",
22	····················"shell.execute_reply":·"2025-12-11T02:55:16.338350Z"	22	····················"shell.execute_reply":·"2024-11-07T21:30:22.743504Z"
23	················}	23	················}
24	············},	24	············},
25	············"outputs":·[],	25	············"outputs":·[],
26	············"source":·[	26	············"source":·[
27	················"import·numpy·as·np\n",	27	················"import·numpy·as·np\n",
28	················"import·pandas·as·pd\n",	28	················"import·pandas·as·pd\n",
29	················"import·statsmodels.api·as·sm"	29	················"import·statsmodels.api·as·sm"
Offset 37, 18 lines modified		Offset 37, 18 lines modified
37	············]	37	············]
38	········},	38	········},
39	········{	39	········{
40	············"cell_type":·"code",	40	············"cell_type":·"code",
41	············"execution_count":·2,	41	············"execution_count":·2,
42	············"metadata":·{	42	············"metadata":·{
43	················"execution":·{	43	················"execution":·{
44	····················"iopub.execute_input":·"2025-12-11T02:55:16.34~~1510~~Z",	44	····················"iopub.execute_input":·"2024-11-07T21:30:22.746967Z",
45	····················"iopub.status.busy":·"2025-12-11T02:55:16.34~~1142~~Z",	45	····················"iopub.status.busy":·"2024-11-07T21:30:22.746699Z",
46	····················"iopub.status.idle":·"2025-12-11T02:55:16.~~343654~~Z",	46	····················"iopub.status.idle":·"2024-11-07T21:30:22.755995Z",
47	····················"shell.execute_reply":·"2025-12-11T02:55:16.~~343318~~Z"	47	····················"shell.execute_reply":·"2024-11-07T21:30:22.755496Z"
48	················}	48	················}
49	············},	49	············},
50	············"outputs":·[],	50	············"outputs":·[],
51	············"source":·[	51	············"source":·[
52	················"p·=·5"	52	················"p·=·5"
53	············]	53	············]
54	········},	54	········},
Offset 60, 18 lines modified		Offset 60, 18 lines modified
60	············]	60	············]
61	········},	61	········},
62	········{	62	········{
63	············"cell_type":·"code",	63	············"cell_type":·"code",
64	············"execution_count":·3,	64	············"execution_count":·3,
65	············"metadata":·{	65	············"metadata":·{
66	················"execution":·{	66	················"execution":·{
67	····················"iopub.execute_input":·"2025-12-11T02:55:16.~~3457~~40Z",	67	····················"iopub.execute_input":·"2024-11-07T21:30:22.758448Z",
68	····················"iopub.status.busy":·"2025-12-11T02:55:16.~~345439~~Z",	68	····················"iopub.status.busy":·"2024-11-07T21:30:22.758257Z",
69	····················"iopub.status.idle":·"2025-12-11T02:55:16.347755Z",	69	····················"iopub.status.idle":·"2024-11-07T21:30:22.767995Z",
70	····················"shell.execute_reply":·"2025-12-11T02:55:16.347425Z"	70	····················"shell.execute_reply":·"2024-11-07T21:30:22.767496Z"
71	················}	71	················}
72	············},	72	············},
73	············"outputs":·[],	73	············"outputs":·[],
74	············"source":·[	74	············"source":·[
75	················"groups_var·=·1\n",	75	················"groups_var·=·1\n",
76	················"level1_var·=·2\n",	76	················"level1_var·=·2\n",
77	················"level2_var·=·3\n",	77	················"level2_var·=·3\n",
Offset 86, 18 lines modified		Offset 86, 18 lines modified
86	············]	86	············]
87	········},	87	········},
88	········{	88	········{
89	············"cell_type":·"code",	89	············"cell_type":·"code",
90	············"execution_count":·4,	90	············"execution_count":·4,
91	············"metadata":·{	91	············"metadata":·{
92	················"execution":·{	92	················"execution":·{
93	····················"iopub.execute_input":·"2025-12-11T02:55:16.~~349818~~Z",	93	····················"iopub.execute_input":·"2024-11-07T21:30:22.770655Z",
94	····················"iopub.status.busy":·"2025-12-11T02:55:16.~~349~~488Z",	94	····················"iopub.status.busy":·"2024-11-07T21:30:22.770470Z",
95	····················"iopub.status.idle":·"2025-12-11T02:55:16.~~357863~~Z",	95	····················"iopub.status.idle":·"2024-11-07T21:30:22.779958Z",
96	····················"shell.execute_reply":·"2025-12-11T02:55:16.~~351680~~Z"	96	····················"shell.execute_reply":·"2024-11-07T21:30:22.779494Z"
97	················}	97	················}
98	············},	98	············},
99	············"outputs":·[],	99	············"outputs":·[],
100	············"source":·[	100	············"source":·[
101	················"n_groups·=·100"	101	················"n_groups·=·100"
102	············]	102	············]
103	········},	103	········},
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109	············]	109	············]
110	········},	110	········},
111	········{	111	········{
112	············"cell_type":·"code",	112	············"cell_type":·"code",
113	············"execution_count":·5,	113	············"execution_count":·5,
114	············"metadata":·{	114	············"metadata":·{
115	················"execution":·{	115	················"execution":·{
116	····················"iopub.execute_input":·"2025-12-11T02:55:16.~~360134~~Z",	116	····················"iopub.execute_input":·"2024-11-07T21:30:22.782669Z",
117	····················"iopub.status.busy":·"2025-12-11T02:55:16.~~3598~~79Z",	117	····················"iopub.status.busy":·"2024-11-07T21:30:22.782478Z",
118	····················"iopub.status.idle":·"2025-12-11T02:55:16.362165Z",	118	····················"iopub.status.idle":·"2024-11-07T21:30:22.796021Z",
119	····················"shell.execute_reply":·"2025-12-11T02:55:16.~~361836~~Z"	119	····················"shell.execute_reply":·"2024-11-07T21:30:22.795510Z"
120	················}	120	················}
121	············},	121	············},
122	············"outputs":·[],	122	············"outputs":·[],
123	············"source":·[	123	············"source":·[
124	················"group_size·=·20\n",	124	················"group_size·=·20\n",
125	················"level1_size·=·10\n",	125	················"level1_size·=·10\n",
126	················"level2_size·=·5"	126	················"level2_size·=·5"
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134	············]	134	············]
135	········},	135	········},
136	········{	136	········{
137	············"cell_type":·"code",	137	············"cell_type":·"code",
138	············"execution_count":·6,	138	············"execution_count":·6,
139	············"metadata":·{	139	············"metadata":·{
140	················"execution":·{	140	················"execution":·{
141	····················"iopub.execute_input":·"2025-12-11T02:55:16.~~364108~~Z",	141	····················"iopub.execute_input":·"2024-11-07T21:30:22.798795Z",
142	····················"iopub.status.busy":·"2025-12-11T02:55:16.~~363849~~Z",	142	····················"iopub.status.busy":·"2024-11-07T21:30:22.798611Z",
143	····················"iopub.status.idle":·"2025-12-11T02:55:16.~~366109~~Z",	143	····················"iopub.status.idle":·"2024-11-07T21:30:22.807934Z",
144	····················"shell.execute_reply":·"2025-12-11T02:55:16.~~365755~~Z"	144	····················"shell.execute_reply":·"2024-11-07T21:30:22.807488Z"
145	················}	145	················}
146	············},	146	············},
147	············"outputs":·[],	147	············"outputs":·[],
148	············"source":·[	148	············"source":·[
149	················"n·=·n_groups··group_size··level1_size·*·level2_size"	149	················"n·=·n_groups··group_size··level1_size·*·level2_size"
150	············]	150	············]
151	········},	151	········},
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157	············]	157	············]
158	········},	158	········},
159	········{	159	········{
160	············"cell_type":·"code",	160	············"cell_type":·"code",
161	············"execution_count":·7,	161	············"execution_count":·7,
162	············"metadata":·{	162	············"metadata":·{
163	················"execution":·{	163	················"execution":·{
164	····················"iopub.execute_input":·"2025-12-11T02:55:16.~~367922~~Z",	164	····················"iopub.execute_input":·"2024-11-07T21:30:22.810405Z",
165	····················"iopub.status.busy":·"2025-12-11T02:55:16.~~367776~~Z",	165	····················"iopub.status.busy":·"2024-11-07T21:30:22.810230Z",
166	····················"iopub.status.idle":·"2025-12-11T02:55:16.~~4289~~64Z",	166	····················"iopub.status.idle":·"2024-11-07T21:30:23.000060Z",
167	····················"shell.execute_reply":·"2025-12-11T02:55:16.~~428~~503Z"	167	····················"shell.execute_reply":·"2024-11-07T21:30:22.999514Z"
168	················}	168	················}
169	············},	169	············},
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14	············]	14	············]
15	········},	15	········},
16	········{	16	········{
17	············"cell_type":·"code",	17	············"cell_type":·"code",
18	············"execution_count":·1,	18	············"execution_count":·1,
19	············"metadata":·{	19	············"metadata":·{
20	················"execution":·{	20	················"execution":·{
21	····················"iopub.execute_input":·"2025-12-11T02:56:17.~~184487~~Z",	21	····················"iopub.execute_input":·"2024-11-07T21:28:27.032775Z",
22	····················"iopub.status.busy":·"2025-12-11T02:56:17.~~184143~~Z",	22	····················"iopub.status.busy":·"2024-11-07T21:28:27.032558Z",
23	····················"iopub.status.idle":·"2025-12-11T02:56:18.637~~905~~Z",	23	····················"iopub.status.idle":·"2024-11-07T21:28:29.363534Z",
24	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~637408~~Z"	24	····················"shell.execute_reply":·"2024-11-07T21:28:29.351525Z"
25	················}	25	················}
26	············},	26	············},
27	············"outputs":·[],	27	············"outputs":·[],
28	············"source":·[	28	············"source":·[
29	················"import·pandas·as·pd\n",	29	················"import·pandas·as·pd\n",
30	················"import·numpy·as·np\n",	30	················"import·numpy·as·np\n",
31	················"from·scipy.stats.distributions·import·norm,·poisson\n",	31	················"from·scipy.stats.distributions·import·norm,·poisson\n",
Offset 42, 18 lines modified		Offset 42, 18 lines modified
42	············]	42	············]
43	········},	43	········},
44	········{	44	········{
45	············"cell_type":·"code",	45	············"cell_type":·"code",
46	············"execution_count":·2,	46	············"execution_count":·2,
47	············"metadata":·{	47	············"metadata":·{
48	················"execution":·{	48	················"execution":·{
49	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~640571~~Z",	49	····················"iopub.execute_input":·"2024-11-07T21:28:29.374134Z",
50	····················"iopub.status.busy":·"2025-12-11T02:56:18.640215Z",	50	····················"iopub.status.busy":·"2024-11-07T21:28:29.372158Z",
51	····················"iopub.status.idle":·"2025-12-11T02:56:18.~~643989~~Z",	51	····················"iopub.status.idle":·"2024-11-07T21:28:29.415557Z",
52	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~643~~598Z"	52	····················"shell.execute_reply":·"2024-11-07T21:28:29.399514Z"
53	················},	53	················},
54	················"lines_to_next_cell":·1	54	················"lines_to_next_cell":·1
55	············},	55	············},
56	············"outputs":·[],	56	············"outputs":·[],
57	············"source":·[	57	············"source":·[
58	················"def·negbinom(u,·mu,·scale):\n",	58	················"def·negbinom(u,·mu,·scale):\n",
59	················"····p·=·(scale·-·1)·/·scale\n",	59	················"····p·=·(scale·-·1)·/·scale\n",
Offset 70, 18 lines modified		Offset 70, 18 lines modified
70	············]	70	············]
71	········},	71	········},
72	········{	72	········{
73	············"cell_type":·"code",	73	············"cell_type":·"code",
74	············"execution_count":·3,	74	············"execution_count":·3,
75	············"metadata":·{	75	············"metadata":·{
76	················"execution":·{	76	················"execution":·{
77	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~646845~~Z",	77	····················"iopub.execute_input":·"2024-11-07T21:28:29.422362Z",
78	····················"iopub.status.busy":·"2025-12-11T02:56:18.~~64606~~1Z",	78	····················"iopub.status.busy":·"2024-11-07T21:28:29.422121Z",
79	····················"iopub.status.idle":·"2025-12-11T02:56:18.~~658065~~Z",	79	····················"iopub.status.idle":·"2024-11-07T21:28:29.429202Z",
80	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~65761~~4Z"	80	····················"shell.execute_reply":·"2024-11-07T21:28:29.428454Z"
81	················}	81	················}
82	············},	82	············},
83	············"outputs":·[],	83	············"outputs":·[],
84	············"source":·[	84	············"source":·[
85	················"#·Sample·size\n",	85	················"#·Sample·size\n",
86	················"n·=·1000\n",	86	················"n·=·1000\n",
87	················"\n",	87	················"\n",
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106	············]	106	············]
107	········},	107	········},
108	········{	108	········{
109	············"cell_type":·"code",	109	············"cell_type":·"code",
110	············"execution_count":·4,	110	············"execution_count":·4,
111	············"metadata":·{	111	············"metadata":·{
112	················"execution":·{	112	················"execution":·{
113	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~66032~~9Z",	113	····················"iopub.execute_input":·"2024-11-07T21:28:29.431569Z",
114	····················"iopub.status.busy":·"2025-12-11T02:56:18.~~6601~~60Z",	114	····················"iopub.status.busy":·"2024-11-07T21:28:29.431363Z",
115	····················"iopub.status.idle":·"2025-12-11T02:56:18.663225Z",	115	····················"iopub.status.idle":·"2024-11-07T21:28:29.437953Z",
116	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~6628~~79Z"	116	····················"shell.execute_reply":·"2024-11-07T21:28:29.437273Z"
117	················}	117	················}
118	············},	118	············},
119	············"outputs":·[],	119	············"outputs":·[],
120	············"source":·[	120	············"source":·[
121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",	121	················"#·Build·a·design·matrix·for·the·alternative·(more·complex)·model\n",
122	················"x·=·np.random.normal(size=(n,·p))\n",	122	················"x·=·np.random.normal(size=(n,·p))\n",
123	················"x[:,·0]·=·1"	123	················"x[:,·0]·=·1"
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131	············]	131	············]
132	········},	132	········},
133	········{	133	········{
134	············"cell_type":·"code",	134	············"cell_type":·"code",
135	············"execution_count":·5,	135	············"execution_count":·5,
136	············"metadata":·{	136	············"metadata":·{
137	················"execution":·{	137	················"execution":·{
138	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~665312~~Z",	138	····················"iopub.execute_input":·"2024-11-07T21:28:29.440275Z",
139	····················"iopub.status.busy":·"2025-12-11T02:56:18.~~665~~032Z",	139	····················"iopub.status.busy":·"2024-11-07T21:28:29.440088Z",
140	····················"iopub.status.idle":·"2025-12-11T02:56:18.~~667354~~Z",	140	····················"iopub.status.idle":·"2024-11-07T21:28:29.444495Z",
141	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~667~~016Z"	141	····················"shell.execute_reply":·"2024-11-07T21:28:29.444087Z"
142	················}	142	················}
143	············},	143	············},
144	············"outputs":·[],	144	············"outputs":·[],
145	············"source":·[	145	············"source":·[
146	················"x0·=·x[:,·0:3]"	146	················"x0·=·x[:,·0:3]"
147	············]	147	············]
148	········},	148	········},
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154	············]	154	············]
155	········},	155	········},
156	········{	156	········{
157	············"cell_type":·"code",	157	············"cell_type":·"code",
158	············"execution_count":·6,	158	············"execution_count":·6,
159	············"metadata":·{	159	············"metadata":·{
160	················"execution":·{	160	················"execution":·{
161	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~669354~~Z",	161	····················"iopub.execute_input":·"2024-11-07T21:28:29.446740Z",
162	····················"iopub.status.busy":·"2025-12-11T02:56:18.~~669092~~Z",	162	····················"iopub.status.busy":·"2024-11-07T21:28:29.446565Z",
163	····················"iopub.status.idle":·"2025-12-11T02:56:18.671~~224~~Z",	163	····················"iopub.status.idle":·"2024-11-07T21:28:29.451972Z",
164	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~670906~~Z"	164	····················"shell.execute_reply":·"2024-11-07T21:28:29.451529Z"
165	················}	165	················}
166	············},	166	············},
167	············"outputs":·[],	167	············"outputs":·[],
168	············"source":·[	168	············"source":·[
169	················"#·Scale·parameter·for·negative·binomial·distribution\n",	169	················"#·Scale·parameter·for·negative·binomial·distribution\n",
170	················"scale·=·10"	170	················"scale·=·10"
171	············]	171	············]
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178	············]	178	············]
179	········},	179	········},
180	········{	180	········{
181	············"cell_type":·"code",	181	············"cell_type":·"code",
182	············"execution_count":·7,	182	············"execution_count":·7,
183	············"metadata":·{	183	············"metadata":·{
184	················"execution":·{	184	················"execution":·{
185	····················"iopub.execute_input":·"2025-12-11T02:56:18.~~673041~~Z",	185	····················"iopub.execute_input":·"2024-11-07T21:28:29.454273Z",
186	····················"iopub.status.busy":·"2025-12-11T02:56:18.~~6728~~90Z",	186	····················"iopub.status.busy":·"2024-11-07T21:28:29.454098Z",
187	····················"iopub.status.idle":·"2025-12-11T02:56:18.~~675980~~Z",	187	····················"iopub.status.idle":·"2024-11-07T21:28:29.464015Z",
188	····················"shell.execute_reply":·"2025-12-11T02:56:18.~~675648~~Z"	188	····················"shell.execute_reply":·"2024-11-07T21:28:29.463491Z"
189	················}	189	················}
190	············},	190	············},
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27	············]	27	············]
28	········},	28	········},
29	········{	29	········{
30	············"cell_type":·"code",	30	············"cell_type":·"code",
31	············"execution_count":·1,	31	············"execution_count":·1,
32	············"metadata":·{	32	············"metadata":·{
33	················"execution":·{	33	················"execution":·{
34	····················"iopub.execute_input":·"2025-12-11T02:55:56.~~056968~~Z",	34	····················"iopub.execute_input":·"2024-11-07T21:30:07.282317Z",
35	····················"iopub.status.busy":·"2025-12-11T02:55:56.~~056703~~Z",	35	····················"iopub.status.busy":·"2024-11-07T21:30:07.282136Z",
36	····················"iopub.status.idle":·"2025-12-11T02:55:57.~~1523~~94Z",	36	····················"iopub.status.idle":·"2024-11-07T21:30:09.009996Z",
37	····················"shell.execute_reply":·"2025-12-11T02:55:57.~~151887~~Z"	37	····················"shell.execute_reply":·"2024-11-07T21:30:09.009460Z"
38	················},	38	················},
39	················"jupyter":·{	39	················"jupyter":·{
40	····················"outputs_hidden":·false	40	····················"outputs_hidden":·false
41	················}	41	················}
42	············},	42	············},
43	············"outputs":·[],	43	············"outputs":·[],
44	············"source":·[	44	············"source":·[
Offset 56, 18 lines modified		Offset 56, 18 lines modified
56	············]	56	············]
57	········},	57	········},
58	········{	58	········{
59	············"cell_type":·"code",	59	············"cell_type":·"code",
60	············"execution_count":·2,	60	············"execution_count":·2,
61	············"metadata":·{	61	············"metadata":·{
62	················"execution":·{	62	················"execution":·{
63	····················"iopub.execute_input":·"2025-12-11T02:55:57.~~178794~~Z",	63	····················"iopub.execute_input":·"2024-11-07T21:30:09.013182Z",
64	····················"iopub.status.busy":·"2025-12-11T02:55:57.178467Z",	64	····················"iopub.status.busy":·"2024-11-07T21:30:09.012892Z",
65	····················"iopub.status.idle":·"2025-12-11T02:55:57.~~196576~~Z",	65	····················"iopub.status.idle":·"2024-11-07T21:30:09.028140Z",
66	····················"shell.execute_reply":·"2025-12-11T02:55:57.~~196131~~Z"	66	····················"shell.execute_reply":·"2024-11-07T21:30:09.027510Z"
67	················},	67	················},
68	················"jupyter":·{	68	················"jupyter":·{
69	····················"outputs_hidden":·false	69	····················"outputs_hidden":·false
70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
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113	············]	113	············]
114	········},	114	········},
115	········{	115	········{
116	············"cell_type":·"code",	116	············"cell_type":·"code",
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23	················"%matplotlib·inline"	23	················"%matplotlib·inline"
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38	············"source":·[	38	············"source":·[
39	················"import·numpy·as·np\n",	39	················"import·numpy·as·np\n",
40	················"import·statsmodels.api·as·sm\n",	40	················"import·statsmodels.api·as·sm\n",
41	················"from·scipy·import·stats\n",	41	················"from·scipy·import·stats\n",
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59	············]	59	············]
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70	················}	70	················}
71	············},	71	············},
72	············"outputs":·[	72	············"outputs":·[
73	················{	73	················{
74	····················"name":·"stdout",	74	····················"name":·"stdout",
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76	····················"text":·[	76	····················"text":·[
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139	················}	139	················}
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143	················"data·=·sm.datasets.star98.load()\n",	143	················"data·=·sm.datasets.star98.load()\n",
144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"	144	················"data.exog·=·sm.add_constant(data.exog,·prepend=False)"
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249	········},	249	········},
250	········{	250	········{
251	············"cell_type":·"code",	251	············"cell_type":·"code",
252	············"execution_count":·7,	252	············"execution_count":·7,
253	············"metadata":·{	253	············"metadata":·{
254	················"execution":·{	254	················"execution":·{
255	····················"iopub.execute_input":·"2025-12-11T02:55:17.~~225633~~Z",	255	····················"iopub.execute_input":·"2024-11-07T21:28:36.770540Z",
256	····················"iopub.status.busy":·"2025-12-11T02:55:17.~~225~~337Z",	256	····················"iopub.status.busy":·"2024-11-07T21:28:36.770313Z",
257	····················"iopub.status.idle":·"2025-12-11T02:55:17.~~247290~~Z",	257	····················"iopub.status.idle":·"2024-11-07T21:28:36.804041Z",
258	····················"shell.execute_reply":·"2025-12-11T02:55:17.~~24691~~0Z"	258	····················"shell.execute_reply":·"2024-11-07T21:28:36.803490Z"
259	················}	259	················}
260	············},	260	············},
261	············"outputs":·[	261	············"outputs":·[
262	················{	262	················{
263	····················"name":·"stdout",	263	····················"name":·"stdout",
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Offset 230, 17 lines modified		Offset 230, 17 lines modified
230	</pre></div></div>	230	</pre></div></div>
231	</div>	231	</div>
232	<div·class="nboutput·nblast·docutils·container">	232	<div·class="nboutput·nblast·docutils·container">
233	<div·class="prompt·empty·docutils·container">	233	<div·class="prompt·empty·docutils·container">
234	</div>	234	</div>
235	<div·class="output_area·stderr·docutils·container">	235	<div·class="output_area·stderr·docutils·container">
236	<div·class="highlight"><pre>	236	<div·class="highlight"><pre>
237	/tmp/ipykernel_~~30235~~/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	237	/tmp/ipykernel_15842/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
238	··print(mod1.params[1])	238	··print(mod1.params[1])
239	/tmp/ipykernel_~~30235~~/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	239	/tmp/ipykernel_15842/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
240	··print(mod2.params[1]·*·2)	240	··print(mod2.params[1]·*·2)
241	</pre></div></div>	241	</pre></div></div>
242	</div>	242	</div>
243	</section>	243	</section>


244	············<div·class="clearer"></div>	244	············<div·class="clearer"></div>


Offset 176, 20 lines modified		Offset 176, 20 lines modified
176	As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half	176	As·expected,·the·coefficient·for·double_it(LOWINC)·in·the·second·model·is·half
177	the·size·of·the·LOWINC·coefficient·from·the·first·model:	177	the·size·of·the·LOWINC·coefficient·from·the·first·model:
178	[4]:	178	[4]:
179	print(mod1.params[1])	179	print(mod1.params[1])
180	print(mod2.params[1]·*·2)	180	print(mod2.params[1]·*·2)
181	-0.020395987154755834	181	-0.020395987154755834
182	-0.020395987154756382	182	-0.020395987154756382
183	/tmp/ipykernel_~~30235~~/1000445862.py:1:·FutureWarning:·Series.__getitem__	183	/tmp/ipykernel_15842/1000445862.py:1:·FutureWarning:·Series.__getitem__
184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	184	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
185	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	185	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
186	access·a·value·by·position,·use·`ser.iloc[pos]`	186	access·a·value·by·position,·use·`ser.iloc[pos]`
187	··print(mod1.params[1])	187	··print(mod1.params[1])
188	/tmp/ipykernel_~~30235~~/1000445862.py:2:·FutureWarning:·Series.__getitem__	188	/tmp/ipykernel_15842/1000445862.py:2:·FutureWarning:·Series.__getitem__
189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	189	treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys
190	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	190	will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To
191	access·a·value·by·position,·use·`ser.iloc[pos]`	191	access·a·value·by·position,·use·`ser.iloc[pos]`
192	··print(mod2.params[1]·*·2)	192	··print(mod2.params[1]·*·2)
193	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	193	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
194	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	194	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8
195	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s	195	····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s


Offset 17, 18 lines modified		Offset 17, 18 lines modified
17	············]	17	············]
18	········},	18	········},
19	········{	19	········{
20	············"cell_type":·"code",	20	············"cell_type":·"code",
21	············"execution_count":·1,	21	············"execution_count":·1,
22	············"metadata":·{	22	············"metadata":·{
23	················"execution":·{	23	················"execution":·{
24	····················"iopub.execute_input":·"2025-12-11T02:55:31.24~~3009~~Z",	24	····················"iopub.execute_input":·"2024-11-07T21:30:02.049357Z",
25	····················"iopub.status.busy":·"2025-12-11T02:55:31.24~~2628~~Z",	25	····················"iopub.status.busy":·"2024-11-07T21:30:02.049152Z",
26	····················"iopub.status.idle":·"2025-12-11T02:55:32.26~~6991~~Z",	26	····················"iopub.status.idle":·"2024-11-07T21:30:04.060248Z",
27	····················"shell.execute_reply":·"2025-12-11T02:55:32.~~266~~523Z"	27	····················"shell.execute_reply":·"2024-11-07T21:30:04.059511Z"
28	················},	28	················},
29	················"jupyter":·{	29	················"jupyter":·{
30	····················"outputs_hidden":·false	30	····················"outputs_hidden":·false
31	················}	31	················}
32	············},	32	············},
33	············"outputs":·[],	33	············"outputs":·[],
34	············"source":·[	34	············"source":·[
Offset 69, 18 lines modified		Offset 69, 18 lines modified
69	············]	69	············]
70	········},	70	········},
71	········{	71	········{
72	············"cell_type":·"code",	72	············"cell_type":·"code",
73	············"execution_count":·2,	73	············"execution_count":·2,
74	············"metadata":·{	74	············"metadata":·{
75	················"execution":·{	75	················"execution":·{
76	····················"iopub.execute_input":·"2025-12-11T02:55:32.26~~961~~9Z",	76	····················"iopub.execute_input":·"2024-11-07T21:30:04.063279Z",
77	····················"iopub.status.busy":·"2025-12-11T02:55:32.26~~928~~2Z",	77	····················"iopub.status.busy":·"2024-11-07T21:30:04.063042Z",
78	····················"iopub.status.idle":·"2025-12-11T02:55:32.~~307443~~Z",	78	····················"iopub.status.idle":·"2024-11-07T21:30:04.144020Z",
79	····················"shell.execute_reply":·"2025-12-11T02:55:32.~~307016~~Z"	79	····················"shell.execute_reply":·"2024-11-07T21:30:04.143487Z"
80	················},	80	················},
81	················"jupyter":·{	81	················"jupyter":·{
82	····················"outputs_hidden":·false	82	····················"outputs_hidden":·false
83	················}	83	················}
84	············},	84	············},
85	············"outputs":·[	85	············"outputs":·[
86	················{	86	················{
Offset 139, 18 lines modified		Offset 139, 18 lines modified
139	············]	139	············]
140	········},	140	········},
141	········{	141	········{
142	············"cell_type":·"code",	142	············"cell_type":·"code",
143	············"execution_count":·3,	143	············"execution_count":·3,
144	············"metadata":·{	144	············"metadata":·{
145	················"execution":·{	145	················"execution":·{
146	····················"iopub.execute_input":·"2025-12-11T02:55:32.~~309818~~Z",	146	····················"iopub.execute_input":·"2024-11-07T21:30:04.146565Z",
147	····················"iopub.status.busy":·"2025-12-11T02:55:32.~~309641~~Z",	147	····················"iopub.status.busy":·"2024-11-07T21:30:04.146372Z",
148	····················"iopub.status.idle":·"2025-12-11T02:55:32.~~352530~~Z",	148	····················"iopub.status.idle":·"2024-11-07T21:30:04.219982Z",
149	····················"shell.execute_reply":·"2025-12-11T02:55:32.352129Z"	149	····················"shell.execute_reply":·"2024-11-07T21:30:04.219492Z"
150	················},	150	················},
151	················"jupyter":·{	151	················"jupyter":·{
152	····················"outputs_hidden":·false	152	····················"outputs_hidden":·false
153	················}	153	················}
154	············},	154	············},
155	············"outputs":·[	155	············"outputs":·[
156	················{	156	················{
Offset 215, 18 lines modified		Offset 215, 18 lines modified
215	············]	215	············]
216	········},	216	········},
217	········{	217	········{
218	············"cell_type":·"code",	218	············"cell_type":·"code",
219	············"execution_count":·4,	219	············"execution_count":·4,
220	············"metadata":·{	220	············"metadata":·{
221	················"execution":·{	221	················"execution":·{
222	····················"iopub.execute_input":·"2025-12-11T02:55:32.~~354999~~Z",	222	····················"iopub.execute_input":·"2024-11-07T21:30:04.222704Z",
223	····················"iopub.status.busy":·"2025-12-11T02:55:32.~~354712~~Z",	223	····················"iopub.status.busy":·"2024-11-07T21:30:04.222509Z",
224	····················"iopub.status.idle":·"2025-12-11T02:55:32.~~360027~~Z",	224	····················"iopub.status.idle":·"2024-11-07T21:30:04.227805Z",
225	····················"shell.execute_reply":·"2025-12-11T02:55:32.~~359663~~Z"	225	····················"shell.execute_reply":·"2024-11-07T21:30:04.227349Z"
226	················},	226	················},
227	················"jupyter":·{	227	················"jupyter":·{
228	····················"outputs_hidden":·false	228	····················"outputs_hidden":·false
229	················}	229	················}
230	············},	230	············},
231	············"outputs":·[	231	············"outputs":·[
232	················{	232	················{
Offset 237, 17 lines modified		Offset 237, 17 lines modified
237	························"-0.020395987154756382\n"	237	························"-0.020395987154756382\n"
238	····················]	238	····················]
239	················},	239	················},
240	················{	240	················{
241	····················"name":·"stderr",	241	····················"name":·"stderr",
242	····················"output_type":·"stream",	242	····················"output_type":·"stream",
243	····················"text":·[	243	····················"text":·[
244	························"/tmp/ipykernel_~~30235~~/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",	244	························"/tmp/ipykernel_15842/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",
245	························"··print(mod1.params[1])\n",	245	························"··print(mod1.params[1])\n",
246	························"/tmp/ipykernel_~~30235~~/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",	246	························"/tmp/ipykernel_15842/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`\n",
247	························"··print(mod2.params[1]·*·2)\n"	247	························"··print(mod2.params[1]·*·2)\n"
248	····················]	248	····················]
249	················}	249	················}
250	············],	250	············],
251	············"source":·[	251	············"source":·[
252	················"print(mod1.params[1])\n",	252	················"print(mod1.params[1])\n",
253	················"print(mod2.params[1]·*·2)"	253	················"print(mod2.params[1]·*·2)"


Offset 18, 18 lines modified		Offset 18, 18 lines modified
18	············]	18	············]
19	········},	19	········},
20	········{	20	········{
21	············"cell_type":·"code",	21	············"cell_type":·"code",
22	············"execution_count":·1,	22	············"execution_count":·1,
23	············"metadata":·{	23	············"metadata":·{
24	················"execution":·{	24	················"execution":·{
25	····················"iopub.execute_input":·"2025-12-11T02:56:05.~~49324~~1Z",	25	····················"iopub.execute_input":·"2024-11-07T21:28:34.559111Z",
26	····················"iopub.status.busy":·"2025-12-11T02:56:05.~~493080~~Z",	26	····················"iopub.status.busy":·"2024-11-07T21:28:34.558794Z",
27	····················"iopub.status.idle":·"2025-12-11T02:56:06.65~~0338~~Z",	27	····················"iopub.status.idle":·"2024-11-07T21:28:36.159624Z",
28	····················"shell.execute_reply":·"2025-12-11T02:56:06.649836Z"	28	····················"shell.execute_reply":·"2024-11-07T21:28:36.158985Z"
29	················}	29	················}
30	············},	30	············},
31	············"outputs":·[],	31	············"outputs":·[],
32	············"source":·[	32	············"source":·[
33	················"import·pandas·as·pd\n",	33	················"import·pandas·as·pd\n",
34	················"import·numpy·as·np\n",	34	················"import·numpy·as·np\n",
35	················"import·statsmodels.api·as·sm\n",	35	················"import·statsmodels.api·as·sm\n",
Offset 44, 18 lines modified		Offset 44, 18 lines modified
44	············]	44	············]
45	········},	45	········},
46	········{	46	········{
47	············"cell_type":·"code",	47	············"cell_type":·"code",
48	············"execution_count":·2,	48	············"execution_count":·2,
49	············"metadata":·{	49	············"metadata":·{
50	················"execution":·{	50	················"execution":·{
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54	····················"shell.execute_reply":·"2025-12-11T02:56:06.655~~995~~Z"	54	····················"shell.execute_reply":·"2024-11-07T21:28:36.195518Z"
55	················}	55	················}
56	············},	56	············},
57	············"outputs":·[],	57	············"outputs":·[],
58	············"source":·[	58	············"source":·[
59	················"np.random.seed(3424)"	59	················"np.random.seed(3424)"
60	············]	60	············]
61	········},	61	········},
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67	············]	67	············]
68	········},	68	········},
69	········{	69	········{
70	············"cell_type":·"code",	70	············"cell_type":·"code",
71	············"execution_count":·3,	71	············"execution_count":·3,
72	············"metadata":·{	72	············"metadata":·{
73	················"execution":·{	73	················"execution":·{
74	····················"iopub.execute_input":·"2025-12-11T02:56:06.~~659089~~Z",	74	····················"iopub.execute_input":·"2024-11-07T21:28:36.200626Z",
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77	····················"shell.execute_reply":·"2025-12-11T02:56:06.~~6609~~13Z"	77	····················"shell.execute_reply":·"2024-11-07T21:28:36.207510Z"
78	················}	78	················}
79	············},	79	············},
80	············"outputs":·[],	80	············"outputs":·[],
81	············"source":·[	81	············"source":·[
82	················"n·=·1000"	82	················"n·=·1000"
83	············]	83	············]
84	········},	84	········},
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90	············]	90	············]
91	········},	91	········},
92	········{	92	········{
93	············"cell_type":·"code",	93	············"cell_type":·"code",
94	············"execution_count":·4,	94	············"execution_count":·4,
95	············"metadata":·{	95	············"metadata":·{
96	················"execution":·{	96	················"execution":·{
97	····················"iopub.execute_input":·"2025-12-11T02:56:06.~~663314~~Z",	97	····················"iopub.execute_input":·"2024-11-07T21:28:36.211069Z",
98	····················"iopub.status.busy":·"2025-12-11T02:56:06.~~6631~~65Z",	98	····················"iopub.status.busy":·"2024-11-07T21:28:36.210869Z",
99	····················"iopub.status.idle":·"2025-12-11T02:56:06.~~666152~~Z",	99	····················"iopub.status.idle":·"2024-11-07T21:28:36.219968Z",
100	····················"shell.execute_reply":·"2025-12-11T02:56:06.~~665788~~Z"	100	····················"shell.execute_reply":·"2024-11-07T21:28:36.219499Z"
101	················},	101	················},
102	················"lines_to_next_cell":·1	102	················"lines_to_next_cell":·1
103	············},	103	············},
104	············"outputs":·[],	104	············"outputs":·[],
105	············"source":·[	105	············"source":·[
106	················"exp·=·np.random.normal(size=n)"	106	················"exp·=·np.random.normal(size=n)"
107	············]	107	············]
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114	············]	114	············]
115	········},	115	········},
116	········{	116	········{
117	············"cell_type":·"code",	117	············"cell_type":·"code",
118	············"execution_count":·5,	118	············"execution_count":·5,
119	············"metadata":·{	119	············"metadata":·{
120	················"execution":·{	120	················"execution":·{
121	····················"iopub.execute_input":·"2025-12-11T02:56:06.~~668648~~Z",	121	····················"iopub.execute_input":·"2024-11-07T21:28:36.222879Z",
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123	····················"iopub.status.idle":·"2025-12-11T02:56:06.~~67484~~8Z",	123	····················"iopub.status.idle":·"2024-11-07T21:28:36.227928Z",
124	····················"shell.execute_reply":·"2025-12-11T02:56:06.~~674466~~Z"	124	····················"shell.execute_reply":·"2024-11-07T21:28:36.227500Z"
125	················},	125	················},
126	················"lines_to_next_cell":·1	126	················"lines_to_next_cell":·1
127	············},	127	············},
128	············"outputs":·[],	128	············"outputs":·[],
129	············"source":·[	129	············"source":·[
130	················"def·gen_mediator():\n",	130	················"def·gen_mediator():\n",
131	················"····mn·=·np.exp(exp)\n",	131	················"····mn·=·np.exp(exp)\n",
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144	············]	144	············]
145	········},	145	········},
146	········{	146	········{
147	············"cell_type":·"code",	147	············"cell_type":·"code",
148	············"execution_count":·6,	148	············"execution_count":·6,
149	············"metadata":·{	149	············"metadata":·{
150	················"execution":·{	150	················"execution":·{
151	····················"iopub.execute_input":·"2025-12-11T02:56:06.~~677104~~Z",	151	····················"iopub.execute_input":·"2024-11-07T21:28:36.230662Z",
152	····················"iopub.status.busy":·"2025-12-11T02:56:06.~~676833~~Z",	152	····················"iopub.status.busy":·"2024-11-07T21:28:36.230484Z",
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154	····················"shell.execute_reply":·"2025-12-11T02:56:06.~~680467~~Z"	154	····················"shell.execute_reply":·"2024-11-07T21:28:36.235554Z"
155	················},	155	················},
156	················"lines_to_next_cell":·1	156	················"lines_to_next_cell":·1
157	············},	157	············},
158	············"outputs":·[],	158	············"outputs":·[],
159	············"source":·[	159	············"source":·[
160	················"def·gen_outcome(otype,·mtime0):\n",	160	················"def·gen_outcome(otype,·mtime0):\n",
161	················"····if·otype·==·\"full\":\n",	161	················"····if·otype·==·\"full\":\n",
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180	············]	180	············]
181	········},	181	········},
182	········{	182	········{
183	············"cell_type":·"code",	183	············"cell_type":·"code",
184	············"execution_count":·7,	184	············"execution_count":·7,
185	············"metadata":·{	185	············"metadata":·{
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187	····················"iopub.execute_input":·"2025-12-11T02:56:06.686246Z",	187	····················"iopub.execute_input":·"2024-11-07T21:28:36.238632Z",
188	····················"iopub.status.busy":·"2025-12-11T02:56:06.~~6859~~58Z",	188	····················"iopub.status.busy":·"2024-11-07T21:28:36.238454Z",
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190	····················"shell.execute_reply":·"2025-12-11T02:56:06.~~688064~~Z"	190	····················"shell.execute_reply":·"2024-11-07T21:28:36.243698Z"
191	················},	191	················},
192	················"lines_to_next_cell":·1	192	················"lines_to_next_cell":·1
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24	············]	24	············]
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26	········{	26	········{
27	············"cell_type":·"code",	27	············"cell_type":·"code",
28	············"execution_count":·1,	28	············"execution_count":·1,
29	············"metadata":·{	29	············"metadata":·{
30	················"execution":·{	30	················"execution":·{
31	····················"iopub.execute_input":·"2025-12-11T02:55:51.2~~05003~~Z",	31	····················"iopub.execute_input":·"2024-11-07T21:28:34.264475Z",
32	····················"iopub.status.busy":·"2025-12-11T02:55:51.204~~697~~Z",	32	····················"iopub.status.busy":·"2024-11-07T21:28:34.264280Z",
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34	····················"shell.execute_reply":·"2025-12-11T02:55:51.~~809972~~Z"	34	····················"shell.execute_reply":·"2024-11-07T21:28:34.951504Z"
35	················}	35	················}
36	············},	36	············},
37	············"outputs":·[],	37	············"outputs":·[],
38	············"source":·[	38	············"source":·[
39	················"%matplotlib·inline"	39	················"%matplotlib·inline"
40	············]	40	············]
41	········},	41	········},
42	········{	42	········{
43	············"cell_type":·"code",	43	············"cell_type":·"code",
44	············"execution_count":·2,	44	············"execution_count":·2,
45	············"metadata":·{	45	············"metadata":·{
46	················"execution":·{	46	················"execution":·{
47	····················"iopub.execute_input":·"2025-12-11T02:55:51.~~81340~~8Z",	47	····················"iopub.execute_input":·"2024-11-07T21:28:34.972398Z",
48	····················"iopub.status.busy":·"2025-12-11T02:55:51.~~813181~~Z",	48	····················"iopub.status.busy":·"2024-11-07T21:28:34.972097Z",
49	····················"iopub.status.idle":·"2025-12-11T02:55:52.~~511041~~Z",	49	····················"iopub.status.idle":·"2024-11-07T21:28:36.179537Z",
50	····················"shell.execute_reply":·"2025-12-11T02:55:52.~~510~~570Z"	50	····················"shell.execute_reply":·"2024-11-07T21:28:36.163525Z"
51	················}	51	················}
52	············},	52	············},
53	············"outputs":·[],	53	············"outputs":·[],
54	············"source":·[	54	············"source":·[
55	················"import·numpy·as·np\n",	55	················"import·numpy·as·np\n",
56	················"import·pandas·as·pd\n",	56	················"import·pandas·as·pd\n",
57	················"from·scipy·import·stats,·optimize\n",	57	················"from·scipy·import·stats,·optimize\n",
Offset 80, 18 lines modified		Offset 80, 18 lines modified
80	············]	80	············]
81	········},	81	········},
82	········{	82	········{
83	············"cell_type":·"code",	83	············"cell_type":·"code",
84	············"execution_count":·3,	84	············"execution_count":·3,
85	············"metadata":·{	85	············"metadata":·{
86	················"execution":·{	86	················"execution":·{
87	····················"iopub.execute_input":·"2025-12-11T02:55:52.~~513~~732Z",	87	····················"iopub.execute_input":·"2024-11-07T21:28:36.182745Z",
88	····················"iopub.status.busy":·"2025-12-11T02:55:52.513217Z",	88	····················"iopub.status.busy":·"2024-11-07T21:28:36.182430Z",
89	····················"iopub.status.idle":·"2025-12-11T02:55:52.~~519656~~Z",	89	····················"iopub.status.idle":·"2024-11-07T21:28:36.227518Z",
90	····················"shell.execute_reply":·"2025-12-11T02:55:52.51~~9315~~Z"	90	····················"shell.execute_reply":·"2024-11-07T21:28:36.214486Z"
91	················}	91	················}
92	············},	92	············},
93	············"outputs":·[	93	············"outputs":·[
94	················{	94	················{
95	····················"data":·{	95	····················"data":·{
96	························"text/plain":·[	96	························"text/plain":·[
97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	97	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
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118	············]	118	············]
119	········},	119	········},
120	········{	120	········{
121	············"cell_type":·"code",	121	············"cell_type":·"code",
122	············"execution_count":·4,	122	············"execution_count":·4,
123	············"metadata":·{	123	············"metadata":·{
124	················"execution":·{	124	················"execution":·{
125	····················"iopub.execute_input":·"2025-12-11T02:55:52.~~521779~~Z",	125	····················"iopub.execute_input":·"2024-11-07T21:28:36.240246Z",
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128	····················"shell.execute_reply":·"2025-12-11T02:55:52.526818Z"	128	····················"shell.execute_reply":·"2024-11-07T21:28:36.258644Z"
129	················}	129	················}
130	············},	130	············},
131	············"outputs":·[	131	············"outputs":·[
132	················{	132	················{
133	····················"data":·{	133	····················"data":·{
134	························"text/plain":·[	134	························"text/plain":·[
135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"	135	····························"['Carroll',·'Grant',·'Peck',·'Donat',·'Stewart',·'Young']"
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149	············]	149	············]
150	········},	150	········},
151	········{	151	········{
152	············"cell_type":·"code",	152	············"cell_type":·"code",
153	············"execution_count":·5,	153	············"execution_count":·5,
154	············"metadata":·{	154	············"metadata":·{
155	················"execution":·{	155	················"execution":·{
156	····················"iopub.execute_input":·"2025-12-11T02:55:52.~~529184~~Z",	156	····················"iopub.execute_input":·"2024-11-07T21:28:36.276620Z",
157	····················"iopub.status.busy":·"2025-12-11T02:55:52.52~~900~~8Z",	157	····················"iopub.status.busy":·"2024-11-07T21:28:36.276385Z",
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159	····················"shell.execute_reply":·"2025-12-11T02:55:52.~~533197~~Z"	159	····················"shell.execute_reply":·"2024-11-07T21:28:36.307535Z"
160	················}	160	················}
161	············},	161	············},
162	············"outputs":·[	162	············"outputs":·[
163	················{	163	················{
164	····················"data":·{	164	····················"data":·{
165	························"text/plain":·[	165	························"text/plain":·[
166	····························"array([120,·130,··80,·400,··95,·170],·dtype=int64)"	166	····························"array([120,·130,··80,·400,··95,·170],·dtype=int64)"
Offset 183, 18 lines modified		Offset 183, 18 lines modified
183	············]	183	············]
184	········},	184	········},
185	········{	185	········{
186	············"cell_type":·"code",	186	············"cell_type":·"code",
187	············"execution_count":·6,	187	············"execution_count":·6,
188	············"metadata":·{	188	············"metadata":·{
189	················"execution":·{	189	················"execution":·{
190	····················"iopub.execute_input":·"2025-12-11T02:55:52.~~536136~~Z",	190	····················"iopub.execute_input":·"2024-11-07T21:28:36.319000Z",
191	····················"iopub.status.busy":·"2025-12-11T02:55:52.535471Z",	191	····················"iopub.status.busy":·"2024-11-07T21:28:36.318753Z",
192	····················"iopub.status.idle":·"2025-12-11T02:55:52.~~539741~~Z",	192	····················"iopub.status.idle":·"2024-11-07T21:28:36.328064Z",
193	····················"shell.execute_reply":·"2025-12-11T02:55:52.~~539363~~Z"	193	····················"shell.execute_reply":·"2024-11-07T21:28:36.327499Z"
194	················}	194	················}
195	············},	195	············},
196	············"outputs":·[],	196	············"outputs":·[],
197	············"source":·[	197	············"source":·[
198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"	198	················"eff,·var_eff·=·effectsize_smd(mean2,·sd2,·nobs2,·mean1,·sd1,·nobs1)"
199	············]	199	············]
200	········},	200	········},
Offset 209, 18 lines modified		Offset 209, 18 lines modified
209	············]	209	············]
210	········},	210	········},
211	········{	211	········{
212	············"cell_type":·"code",	212	············"cell_type":·"code",
213	············"execution_count":·7,	213	············"execution_count":·7,
214	············"metadata":·{	214	············"metadata":·{
215	················"execution":·{	215	················"execution":·{
216	····················"iopub.execute_input":·"2025-12-11T02:55:52.~~541854~~Z",	216	····················"iopub.execute_input":·"2024-11-07T21:28:36.330946Z",
217	····················"iopub.status.busy":·"2025-12-11T02:55:52.~~541~~700Z",	217	····················"iopub.status.busy":·"2024-11-07T21:28:36.330715Z",
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219	····················"shell.execute_reply":·"2025-12-11T02:55:52.55~~361~~5Z"	219	····················"shell.execute_reply":·"2024-11-07T21:28:36.351505Z"
220	················}	220	················}
221	············},	221	············},
222	············"outputs":·[	222	············"outputs":·[
223	················{	223	················{
224	····················"name":·"stdout",	224	····················"name":·"stdout",
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Offset 543, 15 lines modified		Offset 543, 15 lines modified
543	</div>	543	</div>
544	</div>	544	</div>
545	<div·class="nboutput·docutils·container">	545	<div·class="nboutput·docutils·container">
546	<div·class="prompt·empty·docutils·container">	546	<div·class="prompt·empty·docutils·container">
547	</div>	547	</div>
548	<div·class="output_area·stderr·docutils·container">	548	<div·class="output_area·stderr·docutils·container">
549	<div·class="highlight"><pre>	549	<div·class="highlight"><pre>
550	/tmp/ipykernel_~~24213~~/427128218.py:3:·UserWarning:·set_ticklabels()·should·only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a·FixedLocator.	550	/tmp/ipykernel_30190/427128218.py:3:·UserWarning:·set_ticklabels()·should·only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a·FixedLocator.
551	··ax.set_xticklabels(dta.columns.values[::10])	551	··ax.set_xticklabels(dta.columns.values[::10])
552	</pre></div></div>	552	</pre></div></div>
553	</div>	553	</div>
554	<div·class="nboutput·nblast·docutils·container">	554	<div·class="nboutput·nblast·docutils·container">
555	<div·class="prompt·empty·docutils·container">	555	<div·class="prompt·empty·docutils·container">
556	</div>	556	</div>
557	<div·class="output_area·docutils·container">	557	<div·class="output_area·docutils·container">


Offset 126, 15 lines modified		Offset 126, 15 lines modified
126	lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)	126	lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)
127	ax.set_xticklabels(dta.columns.values[::10])	127	ax.set_xticklabels(dta.columns.values[::10])
128	ax.set_xlim(0,·51)	128	ax.set_xlim(0,·51)
129	ax.set_xlabel("Year",·size=17)	129	ax.set_xlabel("Year",·size=17)
130	fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)	130	fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)
131	legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")	131	legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")
132	legend.draw_frame(False)	132	legend.draw_frame(False)
133	/tmp/ipykernel_~~24213~~/427128218.py:3:·UserWarning:·set_ticklabels()·should·only	133	/tmp/ipykernel_30190/427128218.py:3:·UserWarning:·set_ticklabels()·should·only
134	be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a	134	be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a
135	FixedLocator.	135	FixedLocator.
136	··ax.set_xticklabels(dta.columns.values[::10])	136	··ax.set_xticklabels(dta.columns.values[::10])
137	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]	137	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]
138	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories	138	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories
139	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience	139	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience
140	function·produces·such·a·plot.	140	function·produces·such·a·plot.


Offset 481, 17 lines modified		Offset 481, 17 lines modified
481	</div>	481	</div>
482	<div·class="output_area·stderr·docutils·container">	482	<div·class="output_area·stderr·docutils·container">
483	<div·class="highlight"><pre>	483	<div·class="highlight"><pre>
484	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	484	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
485	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	485	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
486	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	486	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
487	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	487	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
488	/tmp/ipykernel_31594/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	488	/tmp/ipykernel_12937/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
489	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"	489	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"
490	/tmp/ipykernel_31594/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	490	/tmp/ipykernel_12937/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
491	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"	491	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"
492	</pre></div></div>	492	</pre></div></div>
493	</div>	493	</div>
494	<div·class="nboutput·docutils·container">	494	<div·class="nboutput·docutils·container">
495	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:	495	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[15]:
496	</pre></div>	496	</pre></div>
497	</div>	497	</div>


Offset 238, 18 lines modified		Offset 238, 18 lines modified

238	#·Show·all·plots.	238	#·Show·all·plots.
239	#·plt.show()	239	#·plt.show()
240	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	240	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
241	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	241	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
242	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'	242	<>:18:·SyntaxWarning:·invalid·escape·sequence·'\$'
243	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'	243	<>:30:·SyntaxWarning:·invalid·escape·sequence·'\$'
244	/tmp/ipykernel_31594/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence	244	/tmp/ipykernel_12937/1205084488.py:18:·SyntaxWarning:·invalid·escape·sequence
245	'\$'	245	'\$'
246	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"	246	··plot_opts["bean_legend_text"]·=·"Income·<·\$30k"
247	/tmp/ipykernel_31594/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence	247	/tmp/ipykernel_12937/1205084488.py:30:·SyntaxWarning:·invalid·escape·sequence
248	'\$'	248	'\$'
249	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"	249	··plot_opts["bean_legend_text"]·=·"Income·>·\$50k"
250	[15]:	250	[15]:
251	Text(0.5,·1.0,·"US·national·election·'96·-·Age·&·Party·Identification")	251	Text(0.5,·1.0,·"US·national·election·'96·-·Age·&·Party·Identification")
252	[../../../_images/examples_notebooks_generated_plots_boxplots_22_2.png]	252	[../../../_images/examples_notebooks_generated_plots_boxplots_22_2.png]
253	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]	253	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x84_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
254	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8	254	\x8\x8\x8\x8·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·\x8\x8\x8\x8


Offset 174, 17 lines modified		Offset 174, 17 lines modified
174	</div>	174	</div>
175	<div·class="output_area·stderr·docutils·container">	175	<div·class="output_area·stderr·docutils·container">
176	<div·class="highlight"><pre>	176	<div·class="highlight"><pre>
177	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	177	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
178	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	178	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
179	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	179	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
180	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	180	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
181	/tmp/ipykernel_1862/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	181	/tmp/ipykernel_31086/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
182	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]	182	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]
183	/tmp/ipykernel_1862/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	183	/tmp/ipykernel_31086/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
184	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]	184	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi··a,·0,·np.pi··a]
185	</pre></div></div>	185	</pre></div></div>
186	</div>	186	</div>
187	<div·class="nboutput·docutils·container">	187	<div·class="nboutput·docutils·container">
188	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:	188	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:
189	</pre></div>	189	</pre></div>
190	</div>	190	</div>


Offset 64, 19 lines modified		Offset 64, 19 lines modified
64	····support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,	64	····support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,
65	np.pi·*·a]	65	np.pi·*·a]
66	)	66	)
67	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	67	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
68	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	68	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
69	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	69	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
70	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'	70	<>:5:·SyntaxWarning:·invalid·escape·sequence·'\p'
71	/tmp/ipykernel_1862/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	71	/tmp/ipykernel_31086/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence
72	'\p'	72	'\p'
73	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi	73	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi
74	*·a]	74	*·a]
75	/tmp/ipykernel_1862/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence	75	/tmp/ipykernel_31086/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence
76	'\p'	76	'\p'
77	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi	77	··support,·andrew.weights,·["$-\pia$",·"0",·"$\pia$"],·[-np.pi·*·a,·0,·np.pi
78	*·a]	78	*·a]
79	[6]:	79	[6]:
80	<Axes:·>	80	<Axes:·>
81	[../../../_images/examples_notebooks_generated_robust_models_1_9_2.png]	81	[../../../_images/examples_notebooks_generated_robust_models_1_9_2.png]
82	\x8\x8\x8\x8\x8·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8¶·\x8\x8\x8\x8\x8	82	\x8\x8\x8\x8\x8·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8¶·\x8\x8\x8\x8\x8


Offset 16, 18 lines modified		Offset 16, 18 lines modified
16	········},	16	········},
17	········{	17	········{
18	············"cell_type":·"code",	18	············"cell_type":·"code",
19	············"execution_count":·1,	19	············"execution_count":·1,
20	············"metadata":·{	20	············"metadata":·{
21	················"collapsed":·false,	21	················"collapsed":·false,
22	················"execution":·{	22	················"execution":·{
23	····················"iopub.execute_input":·"2025-12-11T02:56:20.3~~8254~~1Z",	23	····················"iopub.execute_input":·"2024-11-07T21:29:36.320281Z",
24	····················"iopub.status.busy":·"2025-12-11T02:56:20.3~~82354~~Z",	24	····················"iopub.status.busy":·"2024-11-07T21:29:36.320037Z",
25	····················"iopub.status.idle":·"2025-12-11T02:56:20.~~92212~~9Z",	25	····················"iopub.status.idle":·"2024-11-07T21:29:37.438569Z",
26	····················"shell.execute_reply":·"2025-12-11T02:56:20.921623Z"	26	····················"shell.execute_reply":·"2024-11-07T21:29:37.423525Z"
27	················},	27	················},
28	················"jupyter":·{	28	················"jupyter":·{
29	····················"outputs_hidden":·false	29	····················"outputs_hidden":·false
30	················}	30	················}
31	············},	31	············},
32	············"outputs":·[],	32	············"outputs":·[],
33	············"source":·[	33	············"source":·[
Offset 36, 18 lines modified		Offset 36, 18 lines modified
36	········},	36	········},
37	········{	37	········{
38	············"cell_type":·"code",	38	············"cell_type":·"code",
39	············"execution_count":·2,	39	············"execution_count":·2,
40	············"metadata":·{	40	············"metadata":·{
41	················"collapsed":·false,	41	················"collapsed":·false,
42	················"execution":·{	42	················"execution":·{
43	····················"iopub.execute_input":·"2025-12-11T02:56:20.924~~689~~Z",	43	····················"iopub.execute_input":·"2024-11-07T21:29:37.444496Z",
44	····················"iopub.status.busy":·"2025-12-11T02:56:20.924~~267~~Z",	44	····················"iopub.status.busy":·"2024-11-07T21:29:37.444193Z",
45	····················"iopub.status.idle":·"2025-12-11T02:56:21.~~878~~138Z",	45	····················"iopub.status.idle":·"2024-11-07T21:29:38.744116Z",
46	····················"shell.execute_reply":·"2025-12-11T02:56:21.~~877621~~Z"	46	····················"shell.execute_reply":·"2024-11-07T21:29:38.743505Z"
47	················},	47	················},
48	················"jupyter":·{	48	················"jupyter":·{
49	····················"outputs_hidden":·false	49	····················"outputs_hidden":·false
50	················}	50	················}
51	············},	51	············},
52	············"outputs":·[],	52	············"outputs":·[],
53	············"source":·[	53	············"source":·[
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61	········},	61	········},
62	········{	62	········{
63	············"cell_type":·"code",	63	············"cell_type":·"code",
64	············"execution_count":·3,	64	············"execution_count":·3,
65	············"metadata":·{	65	············"metadata":·{
66	················"collapsed":·false,	66	················"collapsed":·false,
67	················"execution":·{	67	················"execution":·{
68	····················"iopub.execute_input":·"2025-12-11T02:56:21.880654Z",	68	····················"iopub.execute_input":·"2024-11-07T21:29:38.748063Z",
69	····················"iopub.status.busy":·"2025-12-11T02:56:21.~~8804~~03Z",	69	····················"iopub.status.busy":·"2024-11-07T21:29:38.747701Z",
70	····················"iopub.status.idle":·"2025-12-11T02:56:21.~~882926~~Z",	70	····················"iopub.status.idle":·"2024-11-07T21:29:38.756107Z",
71	····················"shell.execute_reply":·"2025-12-11T02:56:21.~~882~~568Z"	71	····················"shell.execute_reply":·"2024-11-07T21:29:38.755505Z"
72	················},	72	················},
73	················"jupyter":·{	73	················"jupyter":·{
74	····················"outputs_hidden":·false	74	····················"outputs_hidden":·false
75	················}	75	················}
76	············},	76	············},
77	············"outputs":·[],	77	············"outputs":·[],
78	············"source":·[	78	············"source":·[
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88	········},	88	········},
89	········{	89	········{
90	············"cell_type":·"code",	90	············"cell_type":·"code",
91	············"execution_count":·4,	91	············"execution_count":·4,
92	············"metadata":·{	92	············"metadata":·{
93	················"collapsed":·false,	93	················"collapsed":·false,
94	················"execution":·{	94	················"execution":·{
95	····················"iopub.execute_input":·"2025-12-11T02:56:21.~~885067~~Z",	95	····················"iopub.execute_input":·"2024-11-07T21:29:38.759426Z",
96	····················"iopub.status.busy":·"2025-12-11T02:56:21.~~884738~~Z",	96	····················"iopub.status.busy":·"2024-11-07T21:29:38.759020Z",
97	····················"iopub.status.idle":·"2025-12-11T02:56:21.~~8891~~32Z",	97	····················"iopub.status.idle":·"2024-11-07T21:29:38.768039Z",
98	····················"shell.execute_reply":·"2025-12-11T02:56:21.~~888779~~Z"	98	····················"shell.execute_reply":·"2024-11-07T21:29:38.767507Z"
99	················},	99	················},
100	················"jupyter":·{	100	················"jupyter":·{
101	····················"outputs_hidden":·false	101	····················"outputs_hidden":·false
102	················}	102	················}
103	············},	103	············},
104	············"outputs":·[	104	············"outputs":·[
105	················{	105	················{
Offset 125, 18 lines modified		Offset 125, 18 lines modified
125	········},	125	········},
126	········{	126	········{
127	············"cell_type":·"code",	127	············"cell_type":·"code",
128	············"execution_count":·5,	128	············"execution_count":·5,
129	············"metadata":·{	129	············"metadata":·{
130	················"collapsed":·false,	130	················"collapsed":·false,
131	················"execution":·{	131	················"execution":·{
132	····················"iopub.execute_input":·"2025-12-11T02:56:21.891~~801~~Z",	132	····················"iopub.execute_input":·"2024-11-07T21:29:38.771560Z",
133	····················"iopub.status.busy":·"2025-12-11T02:56:21.891~~106~~Z",	133	····················"iopub.status.busy":·"2024-11-07T21:29:38.771294Z",
134	····················"iopub.status.idle":·"2025-12-11T02:56:21.8~~97031~~Z",	134	····················"iopub.status.idle":·"2024-11-07T21:29:38.803527Z",
135	····················"shell.execute_reply":·"2025-12-11T02:56:21.~~8966~~33Z"	135	····················"shell.execute_reply":·"2024-11-07T21:29:38.787532Z"
136	················},	136	················},
137	················"jupyter":·{	137	················"jupyter":·{
138	····················"outputs_hidden":·false	138	····················"outputs_hidden":·false
139	················}	139	················}
140	············},	140	············},
141	············"outputs":·[],	141	············"outputs":·[],
142	············"source":·[	142	············"source":·[
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145	········},	145	········},
146	········{	146	········{
147	············"cell_type":·"code",	147	············"cell_type":·"code",
148	············"execution_count":·6,	148	············"execution_count":·6,
149	············"metadata":·{	149	············"metadata":·{
150	················"collapsed":·false,	150	················"collapsed":·false,
151	················"execution":·{	151	················"execution":·{
152	····················"iopub.execute_input":·"2025-12-11T02:56:21.8~~99144~~Z",	152	····················"iopub.execute_input":·"2024-11-07T21:29:38.812269Z",
153	····················"iopub.status.busy":·"2025-12-11T02:56:21.8~~98989~~Z",	153	····················"iopub.status.busy":·"2024-11-07T21:29:38.812036Z",
154	····················"iopub.status.idle":·"2025-12-11T02:56:21.~~909268~~Z",	154	····················"iopub.status.idle":·"2024-11-07T21:29:38.851514Z",
155	····················"shell.execute_reply":·"2025-12-11T02:56:21.~~908878~~Z"	155	····················"shell.execute_reply":·"2024-11-07T21:29:38.839506Z"
156	················},	156	················},
157	················"jupyter":·{	157	················"jupyter":·{
158	····················"outputs_hidden":·false	158	····················"outputs_hidden":·false
159	················}	159	················}
160	············},	160	············},
161	············"outputs":·[],	161	············"outputs":·[],
162	············"source":·[	162	············"source":·[
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166	········},	166	········},
167	········{	167	········{
168	············"cell_type":·"code",	168	············"cell_type":·"code",
169	············"execution_count":·7,	169	············"execution_count":·7,
170	············"metadata":·{	170	············"metadata":·{
171	················"collapsed":·false,	171	················"collapsed":·false,
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174	····················"iopub.status.busy":·"2025-12-11T02:56:21.~~911120~~Z",	174	····················"iopub.status.busy":·"2024-11-07T21:29:38.860061Z",
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176	····················"shell.execute_reply":·"2025-12-11T02:56:22.~~161608~~Z"	176	····················"shell.execute_reply":·"2024-11-07T21:29:39.203543Z"
177	················},	177	················},
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Offset 76, 15 lines modified		Offset 76, 15 lines modified
76	</div>	76	</div>
77	</div>	77	</div>
78	<div·class="nboutput·nblast·docutils·container">	78	<div·class="nboutput·nblast·docutils·container">
79	<div·class="prompt·empty·docutils·container">	79	<div·class="prompt·empty·docutils·container">
80	</div>	80	</div>
81	<div·class="output_area·stderr·docutils·container">	81	<div·class="output_area·stderr·docutils·container">
82	<div·class="highlight"><pre>	82	<div·class="highlight"><pre>
83	/tmp/ipykernel_~~568~~4/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.	83	/tmp/ipykernel_18147/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.
84	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	84	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
85	</pre></div></div>	85	</pre></div></div>
86	</div>	86	</div>
87	<section·id="Introduction">	87	<section·id="Introduction">
88	<h2>Introduction<a·class="headerlink"·href="#Introduction"·title="Link·to·this·heading">¶</a></h2>	88	<h2>Introduction<a·class="headerlink"·href="#Introduction"·title="Link·to·this·heading">¶</a></h2>
89	<p>(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)</p>	89	<p>(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)</p>
90	<p>State·space·models·can·generically·be·written·as·follows·(here·we·focus·on·time-invariant·state·space·models,·but·similar·results·apply·also·to·time-varying·models):</p>	90	<p>State·space·models·can·generically·be·written·as·follows·(here·we·focus·on·time-invariant·state·space·models,·but·similar·results·apply·also·to·time-varying·models):</p>
Offset 331, 19 lines modified		Offset 331, 19 lines modified
331	</pre></div></div>	331	</pre></div></div>
332	</div>	332	</div>
333	<div·class="nboutput·nblast·docutils·container">	333	<div·class="nboutput·nblast·docutils·container">
334	<div·class="prompt·empty·docutils·container">	334	<div·class="prompt·empty·docutils·container">
335	</div>	335	</div>
336	<div·class="output_area·stderr·docutils·container">	336	<div·class="output_area·stderr·docutils·container">
337	<div·class="highlight"><pre>	337	<div·class="highlight"><pre>
338	/tmp/ipykernel_~~568~~4/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	338	/tmp/ipykernel_18147/976557282.py:2:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
339	··print('var.level·····=·%.5f'·%·res.params[0])	339	··print('var.level·····=·%.5f'·%·res.params[0])
340	/tmp/ipykernel_~~568~~4/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	340	/tmp/ipykernel_18147/976557282.py:3:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
341	··print('var.irregular·=·%.5f'·%·res.params[1])	341	··print('var.irregular·=·%.5f'·%·res.params[1])
342	/tmp/ipykernel_~~568~~4/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`	342	/tmp/ipykernel_18147/976557282.py:7:·FutureWarning:·Series.__getitem__·treating·keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always·be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by·position,·use·`ser.iloc[pos]`
343	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))	343	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))
344	</pre></div></div>	344	</pre></div></div>
345	</div>	345	</div>
346	</section>	346	</section>
347	</section>	347	</section>
348	<section·id="Example:-SARIMAX">	348	<section·id="Example:-SARIMAX">
349	<h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>	349	<h2>Example:·SARIMAX<a·class="headerlink"·href="#Example:-SARIMAX"·title="Link·to·this·heading">¶</a></h2>


Offset 12, 15 lines modified		Offset 12, 15 lines modified
12	[1]:	12	[1]:
13	import·numpy·as·np	13	import·numpy·as·np
14	import·pandas·as·pd	14	import·pandas·as·pd
15	import·statsmodels.api·as·sm	15	import·statsmodels.api·as·sm

16	dta·=·sm.datasets.macrodata.load_pandas().data	16	dta·=·sm.datasets.macrodata.load_pandas().data
17	dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	17	dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
18	/tmp/ipykernel_~~568~~4/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will	18	/tmp/ipykernel_18147/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will
19	be·removed·in·a·future·version,·please·use·'QE'·instead.	19	be·removed·in·a·future·version,·please·use·'QE'·instead.
20	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')	20	··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')
21	\x8\x8\x8\x8\x8·I\x8In\x8nt\x8tr\x8ro\x8od\x8du\x8uc\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8¶·\x8\x8\x8\x8\x8	21	\x8\x8\x8\x8\x8·I\x8In\x8nt\x8tr\x8ro\x8od\x8du\x8uc\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8¶·\x8\x8\x8\x8\x8
22	(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)	22	(much·of·this·is·based·on·Harvey·(1989);·see·especially·section·3.4)
23	State·space·models·can·generically·be·written·as·follows·(here·we·focus·on	23	State·space·models·can·generically·be·written·as·follows·(here·we·focus·on
24	time-invariant·state·space·models,·but·similar·results·apply·also·to·time-	24	time-invariant·state·space·models,·but·similar·results·apply·also·to·time-
25	varying·models):	25	varying·models):
Offset 245, 25 lines modified		Offset 245, 25 lines modified
245	Original·model	245	Original·model
246	var.level·····=·0.74469	246	var.level·····=·0.74469
247	var.irregular·=·3.37330	247	var.irregular·=·3.37330

248	Concentrated·model	248	Concentrated·model
249	scale·········=·0.74472	249	scale·········=·0.74472
250	h·*·scale·····=·3.37338	250	h·*·scale·····=·3.37338
251	/tmp/ipykernel_~~568~~4/976557282.py:2:·FutureWarning:·Series.__getitem__·treating	251	/tmp/ipykernel_18147/976557282.py:2:·FutureWarning:·Series.__getitem__·treating
252	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always	252	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always
253	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by	253	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by
254	position,·use·`ser.iloc[pos]`	254	position,·use·`ser.iloc[pos]`
255	··print('var.level·····=·%.5f'·%·res.params[0])	255	··print('var.level·····=·%.5f'·%·res.params[0])
256	/tmp/ipykernel_~~568~~4/976557282.py:3:·FutureWarning:·Series.__getitem__·treating	256	/tmp/ipykernel_18147/976557282.py:3:·FutureWarning:·Series.__getitem__·treating
257	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always	257	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always
258	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by	258	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by
259	position,·use·`ser.iloc[pos]`	259	position,·use·`ser.iloc[pos]`
260	··print('var.irregular·=·%.5f'·%·res.params[1])	260	··print('var.irregular·=·%.5f'·%·res.params[1])
261	/tmp/ipykernel_~~568~~4/976557282.py:7:·FutureWarning:·Series.__getitem__·treating	261	/tmp/ipykernel_18147/976557282.py:7:·FutureWarning:·Series.__getitem__·treating
262	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always	262	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always
263	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by	263	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by
264	position,·use·`ser.iloc[pos]`	264	position,·use·`ser.iloc[pos]`
265	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))	265	··print('h··scale·····=·%.5f'·%·(res_conc.params[0]··res_conc.scale))
266	\x8\x8\x8\x8\x8·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8¶·\x8\x8\x8\x8\x8	266	\x8\x8\x8\x8\x8·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8¶·\x8\x8\x8\x8\x8
267	By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically	267	By·default·in·SARIMAX·models,·the·variance·term·is·chosen·by·numerically
268	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow	268	maximizing·the·likelihood·function,·but·an·option·has·been·added·to·allow


Offset 8, 26 lines modified		Offset 8, 26 lines modified
8	············]	8	············]
9	········},	9	········},
10	········{	10	········{
11	············"cell_type":·"code",	11	············"cell_type":·"code",
12	············"execution_count":·1,	12	············"execution_count":·1,
13	············"metadata":·{	13	············"metadata":·{
14	················"execution":·{	14	················"execution":·{
15	····················"iopub.execute_input":·"2025-12-11T02:56:28.~~18457~~9Z",	15	····················"iopub.execute_input":·"2024-11-07T21:30:11.512169Z",
16	····················"iopub.status.busy":·"2025-12-11T02:56:28.~~184311~~Z",	16	····················"iopub.status.busy":·"2024-11-07T21:30:11.511962Z",
17	····················"iopub.status.idle":·"2025-12-11T02:56:28.~~96912~~4Z",	17	····················"iopub.status.idle":·"2024-11-07T21:30:13.223974Z",
18	····················"shell.execute_reply":·"2025-12-11T02:56:28.~~96870~~3Z"	18	····················"shell.execute_reply":·"2024-11-07T21:30:13.223483Z"
19	················}	19	················}
20	············},	20	············},
21	············"outputs":·[	21	············"outputs":·[
22	················{	22	················{
23	····················"name":·"stderr",	23	····················"name":·"stderr",
24	····················"output_type":·"stream",	24	····················"output_type":·"stream",
25	····················"text":·[	25	····················"text":·[
26	························"/tmp/ipykernel_~~568~~4/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.\n",	26	························"/tmp/ipykernel_18147/2378637424.py:6:·FutureWarning:·'Q'·is·deprecated·and·will·be·removed·in·a·future·version,·please·use·'QE'·instead.\n",
27	························"··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')\n"	27	························"··dta.index·=·pd.date_range(start='1959Q1',·end='2009Q4',·freq='Q')\n"
28	····················]	28	····················]
29	················}	29	················}
30	············],	30	············],
31	············"source":·[	31	············"source":·[
32	················"import·numpy·as·np\n",	32	················"import·numpy·as·np\n",
33	················"import·pandas·as·pd\n",	33	················"import·pandas·as·pd\n",
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89	············]	89	············]
90	········},	90	········},
91	········{	91	········{
92	············"cell_type":·"code",	92	············"cell_type":·"code",
93	············"execution_count":·2,	93	············"execution_count":·2,
94	············"metadata":·{	94	············"metadata":·{
95	················"execution":·{	95	················"execution":·{
96	····················"iopub.execute_input":·"2025-12-11T02:56:28.~~97187~~5Z",	96	····················"iopub.execute_input":·"2024-11-07T21:30:13.226665Z",
97	····················"iopub.status.busy":·"2025-12-11T02:56:28.~~971220~~Z",	97	····················"iopub.status.busy":·"2024-11-07T21:30:13.226467Z",
98	····················"iopub.status.idle":·"2025-12-11T02:56:28.~~9795~~16Z",	98	····················"iopub.status.idle":·"2024-11-07T21:30:13.235914Z",
99	····················"shell.execute_reply":·"2025-12-11T02:56:28.~~979136~~Z"	99	····················"shell.execute_reply":·"2024-11-07T21:30:13.235480Z"
100	················}	100	················}
101	············},	101	············},
102	············"outputs":·[],	102	············"outputs":·[],
103	············"source":·[	103	············"source":·[
104	················"class·LocalLevel(sm.tsa.statespace.MLEModel):\n",	104	················"class·LocalLevel(sm.tsa.statespace.MLEModel):\n",
105	················"····_start_params·=·[1.,·1.]\n",	105	················"····_start_params·=·[1.,·1.]\n",
106	················"····_param_names·=·['var.level',·'var.irregular']\n",	106	················"····_param_names·=·['var.level',·'var.irregular']\n",
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135	············]	135	············]
136	········},	136	········},
137	········{	137	········{
138	············"cell_type":·"code",	138	············"cell_type":·"code",
139	············"execution_count":·3,	139	············"execution_count":·3,
140	············"metadata":·{	140	············"metadata":·{
141	················"execution":·{	141	················"execution":·{
142	····················"iopub.execute_input":·"2025-12-11T02:56:28.~~981650~~Z",	142	····················"iopub.execute_input":·"2024-11-07T21:30:13.238287Z",
143	····················"iopub.status.busy":·"2025-12-11T02:56:28.981370Z",	143	····················"iopub.status.busy":·"2024-11-07T21:30:13.238104Z",
144	····················"iopub.status.idle":·"2025-12-11T02:56:29.~~01043~~4Z",	144	····················"iopub.status.idle":·"2024-11-07T21:30:13.295894Z",
145	····················"shell.execute_reply":·"2025-12-11T02:56:29.~~010008~~Z"	145	····················"shell.execute_reply":·"2024-11-07T21:30:13.289636Z"
146	················}	146	················}
147	············},	147	············},
148	············"outputs":·[	148	············"outputs":·[
149	················{	149	················{
150	····················"name":·"stdout",	150	····················"name":·"stdout",
151	····················"output_type":·"stream",	151	····················"output_type":·"stream",
152	····················"text":·[	152	····················"text":·[
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191	········},	191	········},
192	········{	192	········{
193	············"cell_type":·"code",	193	············"cell_type":·"code",
194	············"execution_count":·4,	194	············"execution_count":·4,
195	············"metadata":·{	195	············"metadata":·{
196	················"execution":·{	196	················"execution":·{
197	····················"iopub.execute_input":·"2025-12-11T02:56:29.~~012485~~Z",	197	····················"iopub.execute_input":·"2024-11-07T21:30:13.299702Z",
198	····················"iopub.status.busy":·"2025-12-11T02:56:29.~~0123~~37Z",	198	····················"iopub.status.busy":·"2024-11-07T21:30:13.299437Z",
199	····················"iopub.status.idle":·"2025-12-11T02:56:29.~~016~~441Z",	199	····················"iopub.status.idle":·"2024-11-07T21:30:13.304439Z",
200	····················"shell.execute_reply":·"2025-12-11T02:56:29.~~016~~083Z"	200	····················"shell.execute_reply":·"2024-11-07T21:30:13.304004Z"
201	················}	201	················}
202	············},	202	············},
203	············"outputs":·[	203	············"outputs":·[
204	················{	204	················{
205	····················"name":·"stdout",	205	····················"name":·"stdout",
206	····················"output_type":·"stream",	206	····················"output_type":·"stream",
207	····················"text":·[	207	····················"text":·[
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244	············]	244	············]
245	········},	245	········},
246	········{	246	········{
247	············"cell_type":·"code",	247	············"cell_type":·"code",
248	············"execution_count":·5,	248	············"execution_count":·5,
249	············"metadata":·{	249	············"metadata":·{
250	················"execution":·{	250	················"execution":·{
251	····················"iopub.execute_input":·"2025-12-11T02:56:29.~~019270~~Z",	251	····················"iopub.execute_input":·"2024-11-07T21:30:13.307013Z",
252	····················"iopub.status.busy":·"2025-12-11T02:56:29.018499Z",	252	····················"iopub.status.busy":·"2024-11-07T21:30:13.306835Z",
253	····················"iopub.status.idle":·"2025-12-11T02:56:29.~~026~~003Z",	253	····················"iopub.status.idle":·"2024-11-07T21:30:13.315014Z",
254	····················"shell.execute_reply":·"2025-12-11T02:56:29.~~025606~~Z"	254	····················"shell.execute_reply":·"2024-11-07T21:30:13.314511Z"
255	················}	255	················}
256	············},	256	············},
257	············"outputs":·[],	257	············"outputs":·[],
258	············"source":·[	258	············"source":·[
259	················"class·LocalLevelConcentrated(sm.tsa.statespace.MLEModel):\n",	259	················"class·LocalLevelConcentrated(sm.tsa.statespace.MLEModel):\n",
260	················"····_start_params·=·[1.]\n",	260	················"····_start_params·=·[1.]\n",
261	················"····_param_names·=·['ratio.irregular']\n",	261	················"····_param_names·=·['ratio.irregular']\n",
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289	············]	289	············]
290	········},	290	········},
291	········{	291	········{
292	············"cell_type":·"code",	292	············"cell_type":·"code",
293	············"execution_count":·6,	293	············"execution_count":·6,
294	············"metadata":·{	294	············"metadata":·{
295	················"execution":·{	295	················"execution":·{
296	····················"iopub.execute_input":·"2025-12-11T02:56:29.~~0280~~39Z",	296	····················"iopub.execute_input":·"2024-11-07T21:30:13.317936Z",
297	····················"iopub.status.busy":·"2025-12-11T02:56:29.027~~808~~Z",	297	····················"iopub.status.busy":·"2024-11-07T21:30:13.317756Z",
298	····················"iopub.status.idle":·"2025-12-11T02:56:29.~~051894~~Z",	298	····················"iopub.status.idle":·"2024-11-07T21:30:13.348007Z",
299	····················"shell.execute_reply":·"2025-12-11T02:56:29.~~05151~~3Z"	299	····················"shell.execute_reply":·"2024-11-07T21:30:13.347493Z"
300	················}	300	················}
301	············},	301	············},
302	············"outputs":·[	302	············"outputs":·[
303	················{	303	················{
304	····················"name":·"stdout",	304	····················"name":·"stdout",
305	····················"output_type":·"stream",	305	····················"output_type":·"stream",
306	····················"text":·[	306	····················"text":·[
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351	········},	351	········},
352	········{	352	········{
353	············"cell_type":·"code",	353	············"cell_type":·"code",
354	············"execution_count":·7,	354	············"execution_count":·7,
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132	</div>	132	</div>
133	</div>	133	</div>
134	<div·class="nboutput·nblast·docutils·container">	134	<div·class="nboutput·nblast·docutils·container">
135	<div·class="prompt·empty·docutils·container">	135	<div·class="prompt·empty·docutils·container">
136	</div>	136	</div>
137	<div·class="output_area·docutils·container">	137	<div·class="output_area·docutils·container">
138	<div·class="highlight"><pre>	138	<div·class="highlight"><pre>
		139	·······························SARIMAX·Results
		140	==============================================================================
		141	Dep.·Variable:···················infl···No.·Observations:··················203
		142	Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714
		143	Date:················Sat,·05·Oct·2024···AIC····························951.427
		144	Time:························10:43:25···BIC····························961.367
		145	Sample:····················03-31-1959···HQIC···························955.449
		146	·························-·09-30-2009
		147	Covariance·Type:··················opg
		148	==============================================================================
		149	·················coef····std·err··········z······P>\|z\|······[0.025······0.975]
		150	------------------------------------------------------------------------------
		151	intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895
		152	ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721
		153	sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930
		154	===================================================================================
		155	Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB):················68.45
		156	Prob(Q):······························0.00···Prob(JB):·························0.00
		157	Heteroskedasticity·(H):···············1.47···Skew:····························-0.22
		158	Prob(H)·(two-sided):··················0.12···Kurtosis:·························5.81
		159	===================================================================================

		160	Warnings:
		161	[1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex-step).
139	RUNNING·THE·L-BFGS-B·CODE	162	RUNNING·THE·L-BFGS-B·CODE

140	·············*	163	·············*

141	Machine·precision·=·2.220D-16	164	Machine·precision·=·2.220D-16
142	·N·=············3·····M·=···········10	165	·N·=············3·····M·=···········10
143	·This·problem·is·unconstrained.	166	·This·problem·is·unconstrained.
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163	·············*	187	·············*

164	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	188	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
165	····3······8·····10······1·····0·····0···5.820D-06···2.329D+00	189	····3······8·····10······1·····0·····0···5.820D-06···2.329D+00
166	··F·=···2.3286389358138613	190	··F·=···2.3286389358138613

167	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	191	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
168	·······························SARIMAX·Results
169	==============================================================================
170	Dep.·Variable:···················infl···No.·Observations:··················203
171	Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714
172	Date:················Sat,·05·Oct·2024···AIC····························951.427
173	Time:························10:43:25···BIC····························961.367
174	Sample:····················03-31-1959···HQIC···························955.449
175	·························-·09-30-2009
176	Covariance·Type:··················opg
177	==============================================================================
178	·················coef····std·err··········z······P>\|z\|······[0.025······0.975]
179	------------------------------------------------------------------------------
180	intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895
181	ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721
182	sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930
183	===================================================================================
184	Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB):················68.45
185	Prob(Q):······························0.00···Prob(JB):·························0.00
186	Heteroskedasticity·(H):···············1.47···Skew:····························-0.22
187	Prob(H)·(two-sided):··················0.12···Kurtosis:·························5.81
188	===================================================================================

189	Warnings:
190	[1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex-step).
191	</pre></div></div>	192	</pre></div></div>
192	</div>	193	</div>
193	</section>	194	</section>
194	<section·id="Forecasting">	195	<section·id="Forecasting">
195	<h3>Forecasting<a·class="headerlink"·href="#Forecasting"·title="Link·to·this·heading">¶</a></h3>	196	<h3>Forecasting<a·class="headerlink"·href="#Forecasting"·title="Link·to·this·heading">¶</a></h3>
196	<p>Out-of-sample·forecasts·are·produced·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·or·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·methods·from·the·results·object.</p>	197	<p>Out-of-sample·forecasts·are·produced·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·or·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·methods·from·the·results·object.</p>
197	<p>The·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·method·gives·only·point·forecasts.</p>	198	<p>The·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·method·gives·only·point·forecasts.</p>
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394	</div>	394	</div>
395	</div>	395	</div>
396	<div·class="nboutput·nblast·docutils·container">	396	<div·class="nboutput·nblast·docutils·container">
397	<div·class="prompt·empty·docutils·container">	397	<div·class="prompt·empty·docutils·container">
398	</div>	398	</div>
399	<div·class="output_area·docutils·container">	399	<div·class="output_area·docutils·container">
400	<div·class="highlight"><pre>	400	<div·class="highlight"><pre>
		401	intercept····1.162076
		402	ar.L1········0.724242
		403	sigma2·······5.051600
		404	dtype:·float64
401	RUNNING·THE·L-BFGS-B·CODE	405	RUNNING·THE·L-BFGS-B·CODE

402	·············*	406	·············*

403	Machine·precision·=·2.220D-16	407	Machine·precision·=·2.220D-16
404	·N·=············3·····M·=···········10	408	·N·=············3·····M·=···········10
405	·This·problem·is·unconstrained.	409	·This·problem·is·unconstrained.
Offset 425, 18 lines modified		Offset 429, 14 lines modified
425	·············*	429	·············*

426	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F	430	···N····Tit·····Tnf··Tnint··Skip··Nact·····Projg········F
427	····3······6······8······1·····0·····0···7.066D-07···2.231D+00	431	····3······6······8······1·····0·····0···7.066D-07···2.231D+00
428	··F·=···2.2310884444664767	432	··F·=···2.2310884444664767

429	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL	433	CONVERGENCE:·NORM_OF_PROJECTED_GRADIENT_<=_PGTOL
430	intercept····1.162076
431	ar.L1········0.724242
432	sigma2·······5.051600
433	dtype:·float64
434	</pre></div></div>	434	</pre></div></div>
435	</div>	435	</div>
436	<div·class="nbinput·docutils·container">	436	<div·class="nbinput·docutils·container">
437	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[12]:	437	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[12]:
438	</pre></div>	438	</pre></div>
439	</div>	439	</div>
440	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Step·2:·produce·one-step-ahead·forecasts</span>	440	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Step·2:·produce·one-step-ahead·forecasts</span>
Offset 482, 14 lines modified		Offset 482, 18 lines modified
482	</div>	482	</div>
483	</div>	483	</div>
484	<div·class="nboutput·nblast·docutils·container">	484	<div·class="nboutput·nblast·docutils·container">
485	<div·class="prompt·empty·docutils·container">	485	<div·class="prompt·empty·docutils·container">
486	</div>	486	</div>
487	<div·class="output_area·docutils·container">	487	<div·class="output_area·docutils·container">
488	<div·class="highlight"><pre>	488	<div·class="highlight"><pre>
		489	intercept····1.171544
		490	ar.L1········0.723152
		491	sigma2·······5.024580
		492	dtype:·float64
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