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1	-rw-r--r--···0········0········0········4·2024-01-21·09:38:29.000000·debian-binary	1	-rw-r--r--···0········0········0········4·2024-01-21·09:38:29.000000·debian-binary
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1	Package:·python-statsmodels-doc	1	Package:·python-statsmodels-doc
2	Source:·statsmodels	2	Source:·statsmodels
3	Version:·0.14.1+dfsg-2	3	Version:·0.14.1+dfsg-2
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:·155~~904~~	6	Installed-Size:·155896
7	Depends:·libjs-sphinxdoc·(>=·7.2.2),·libjs-requirejs,·libjs-mathjax	7	Depends:·libjs-sphinxdoc·(>=·7.2.2),·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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7259	usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/mediation_survival.html	7259	usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/mediation_survival.html
7260	usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/mediation_survival.ipynb.gz
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7265	usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/mstl_decomposition.html	7264	usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/mstl_decomposition.html
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23	················"import·matplotlib.pyplot·as·plt\n",	23	················"import·matplotlib.pyplot·as·plt\n",
24	················"import·numpy·as·np\n",	24	················"import·numpy·as·np\n",
25	················"import·seaborn·as·sns\n",	25	················"import·seaborn·as·sns\n",


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37	········},	37	········},
38	········{	38	········{
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40	············"execution_count":·1,	40	············"execution_count":·1,
41	············"id":·"eed890e6",	41	············"id":·"eed890e6",
42	············"metadata":·{	42	············"metadata":·{
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51	············"source":·[	51	············"source":·[
52	················"import·numpy·as·np\n",	52	················"import·numpy·as·np\n",
53	················"import·pandas·as·pd\n",	53	················"import·pandas·as·pd\n",
54	················"\n",	54	················"\n",


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37	················"%matplotlib·inline"	37	················"%matplotlib·inline"
38	············]	38	············]
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49	················}	49	················}
50	············},	50	············},
51	············"outputs":·[],	51	············"outputs":·[],
52	············"source":·[	52	············"source":·[
53	················"import·matplotlib.pyplot·as·plt\n",	53	················"import·matplotlib.pyplot·as·plt\n",
54	················"import·numpy·as·np\n",	54	················"import·numpy·as·np\n",
55	················"import·pandas·as·pd\n",	55	················"import·pandas·as·pd\n",


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10	············]	10	············]
11	········},	11	········},
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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",


Offset 454, 23 lines modified		Offset 454, 14 lines modified
454	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>	454	<span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">()</span>
455	</pre></div>	455	</pre></div>
456	</div>	456	</div>
457	</div>	457	</div>
458	<div·class="nboutput·docutils·container">	458	<div·class="nboutput·docutils·container">
459	<div·class="prompt·empty·docutils·container">	459	<div·class="prompt·empty·docutils·container">
460	</div>	460	</div>
461	<div·class="output_area·stderr·docutils·container">
462	<div·class="highlight"><pre>
463	/usr/lib/python3/dist-packages/statsmodels/tsa/exponential_smoothing/ets.py:437:·UserWarning:·ETSModel·can·give·wrong·results·on·32·bit·i386
464	··warnings.warn(warn_ets)
465	</pre></div></div>
466	</div>
467	<div·class="nboutput·docutils·container">
468	<div·class="prompt·empty·docutils·container">
469	</div>
470	<div·class="output_area·docutils·container">	461	<div·class="output_area·docutils·container">
471	<div·class="highlight"><pre>	462	<div·class="highlight"><pre>
472	RUNNING·THE·L-BFGS-B·CODE	463	RUNNING·THE·L-BFGS-B·CODE

473	·············*	464	·············*

474	Machine·precision·=·2.220D-16	465	Machine·precision·=·2.220D-16


Offset 119, 17 lines modified		Offset 119, 14 lines modified
119	#·obtained·from·R	119	#·obtained·from·R
120	params_R·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,	120	params_R·=·[0.99989969,·0.11888177503085334,·0.80000197,·36.46466837,
121	34.72584983]	121	34.72584983]
122	yhat·=·model.smooth(params_R).fittedvalues	122	yhat·=·model.smooth(params_R).fittedvalues
123	yhat.plot(label="R·fit",·linestyle="--")	123	yhat.plot(label="R·fit",·linestyle="--")

124	plt.legend()	124	plt.legend()
125	/usr/lib/python3/dist-packages/statsmodels/tsa/exponential_smoothing/ets.py:
126	437:·UserWarning:·ETSModel·can·give·wrong·results·on·32·bit·i386
127	··warnings.warn(warn_ets)
128	RUNNING·THE·L-BFGS-B·CODE	125	RUNNING·THE·L-BFGS-B·CODE

129	·············*	126	·············*

130	Machine·precision·=·2.220D-16	127	Machine·precision·=·2.220D-16
131	·N·=············2·····M·=···········10	128	·N·=············2·····M·=···········10


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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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7282	-rw-r--r--···0·root·········(0)·root·········(0)····62934·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressions.html	7282	-rw-r--r--···0·root·········(0)·root·········(0)····62934·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressions.html
7283	-rw-r--r--···0·root·········(0)·root·········(0)····65841·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.html	7283	-rw-r--r--···0·root·········(0)·root·········(0)····65841·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/autoregressive_distributed_lag.html
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7285	-rw-r--r--···0·root·········(0)·root·········(0)····19350·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.html	7285	-rw-r--r--···0·root·········(0)·root·········(0)····19350·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.html
7286	-rw-r--r--···0·root·········(0)·root·········(0)····22146·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.ipynb.gz	7286	-rw-r--r--···0·root·········(0)·root·········(0)····22135·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/categorical_interaction_plot.ipynb.gz
7287	-rw-r--r--···0·root·········(0)·root·········(0)····35056·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.html	7287	-rw-r--r--···0·root·········(0)·root·········(0)····35056·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.html
7288	-rw-r--r--···0·root·········(0)·root·········(0)·····3585·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.ipynb.gz	7288	-rw-r--r--···0·root·········(0)·root·········(0)·····3575·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/chi2_fitting.ipynb.gz
7289	-rw-r--r--···0·root·········(0)·root·········(0)····50454·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/contrasts.html	7289	-rw-r--r--···0·root·········(0)·root·········(0)····50454·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/contrasts.html
7290	-rw-r--r--···0·root·········(0)·root·········(0)····31129·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.html	7290	-rw-r--r--···0·root·········(0)·root·········(0)····31129·2024-01-21·09:38:29.000000·./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/copula.html
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486	······<th></th>	486	······<th></th>
487	······<th>Variance</th>	487	······<th>Variance</th>
488	····</tr>	488	····</tr>
489	··</thead>	489	··</thead>
490	··<tbody>	490	··<tbody>
491	····<tr>	491	····<tr>
492	······<th>groups_ix</th>	492	······<th>groups_ix</th>
493	······<td>0.~~943567~~</td>	493	······<td>1.015931</td>
494	····</tr>	494	····</tr>
495	····<tr>	495	····<tr>
496	······<th>level1_ix</th>	496	······<th>level1_ix</th>
497	······<td>2.0~~6102~~9</td>	497	······<td>2.047519</td>
498	····</tr>	498	····</tr>
499	····<tr>	499	····<tr>
500	······<th>level2_ix</th>	500	······<th>level2_ix</th>
501	······<td>3.~~073325~~</td>	501	······<td>2.988207</td>
502	····</tr>	502	····</tr>
503	····<tr>	503	····<tr>
504	······<th>Residual</th>	504	······<th>Residual</th>
505	······<td>3.96~~6661~~</td>	505	······<td>3.969545</td>
506	····</tr>	506	····</tr>
507	··</tbody>	507	··</tbody>
508	</table>	508	</table>
509	</div></div>	509	</div></div>
510	</div>	510	</div>
511	</section>	511	</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\|_\x80_.._.9_.4_.3_.5_.6_.7\|	86	\|_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x81_.._.0_.1_.5_.9_.3_.1\|
87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x80_\x86_.1_.0_.2_\x89\|	87	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_\x8._\x80_\x84_.7_.5_.1_\x89\|
88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x83_.._.0_.7_.3_.3_.2_.5\|	88	\|_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8\|_\x82_.._.9_.8_.8_.2_.0_.7\|
89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x83_\x8._\x89_\x86_\x86_.6_.6_.1\|	89	\|_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8\|_\x83_\x8._\x89_\x86_\x89_.5_.4_.5\|
90	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8]	90	_\x8[_\x8L_\x8o_\x8g_\x8o_\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 631, 15 lines modified		Offset 631, 15 lines modified
631	</pre></div></div>	631	</pre></div></div>
632	</div>	632	</div>
633	<div·class="nboutput·nblast·docutils·container">	633	<div·class="nboutput·nblast·docutils·container">
634	<div·class="prompt·empty·docutils·container">	634	<div·class="prompt·empty·docutils·container">
635	</div>	635	</div>
636	<div·class="output_area·stderr·docutils·container">	636	<div·class="output_area·stderr·docutils·container">
637	<div·class="highlight"><pre>	637	<div·class="highlight"><pre>
638	/tmp/ipykernel_645/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use·float(ser.iloc[0])·instead	638	/tmp/ipykernel_5148/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single·element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use·float(ser.iloc[0])·instead
639	··print("%2.4f%%"·%·(diff*100))	639	··print("%2.4f%%"·%·(diff*100))
640	</pre></div></div>	640	</pre></div></div>
641	</div>	641	</div>
642	</section>	642	</section>
643	<section·id="Plots">	643	<section·id="Plots">
644	<h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3>	644	<h3>Plots<a·class="headerlink"·href="#Plots"·title="Link·to·this·heading">¶</a></h3>
645	<p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p>	645	<p>We·extract·information·that·will·be·used·to·draw·some·interesting·plots:</p>


Offset 26, 18 lines modified		Offset 26, 18 lines modified
26	············"execution_count":·1,	26	············"execution_count":·1,
27	············"metadata":·{	27	············"metadata":·{
28	················"ExecuteTime":·{	28	················"ExecuteTime":·{
29	····················"end_time":·"2017-12-07T12:39:15.020317Z",	29	····················"end_time":·"2017-12-07T12:39:15.020317Z",
30	····················"start_time":·"2017-12-07T12:39:14.263100Z"	30	····················"start_time":·"2017-12-07T12:39:14.263100Z"
31	················},	31	················},
32	················"execution":·{	32	················"execution":·{
33	····················"iopub.execute_input":·"2024-02-14T01:40:14.~~062178~~Z",	33	····················"iopub.execute_input":·"2025-03-18T13:29:16.995657Z",
34	····················"iopub.status.busy":·"2024-02-14T01:40:14.~~061638~~Z",	34	····················"iopub.status.busy":·"2025-03-18T13:29:16.995277Z",
35	····················"iopub.status.idle":·"2024-02-14T01:40:16.~~849749~~Z",	35	····················"iopub.status.idle":·"2025-03-18T13:29:18.700212Z",
36	····················"shell.execute_reply":·"2024-02-14T01:40:16.~~848280~~Z"	36	····················"shell.execute_reply":·"2025-03-18T13:29:18.699147Z"
37	················}	37	················}
38	············},	38	············},
39	············"outputs":·[],	39	············"outputs":·[],
40	············"source":·[	40	············"source":·[
41	················"import·os\n",	41	················"import·os\n",
42	················"import·numpy·as·np\n",	42	················"import·numpy·as·np\n",
43	················"import·pandas·as·pd\n",	43	················"import·pandas·as·pd\n",


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":·"2024-02-14T01:38:53.~~382159~~Z",	19	····················"iopub.execute_input":·"2025-03-18T13:29:17.054280Z",
20	····················"iopub.status.busy":·"2024-02-14T01:38:53.~~381599~~Z",	20	····················"iopub.status.busy":·"2025-03-18T13:29:17.053871Z",
21	····················"iopub.status.idle":·"2024-02-14T01:38:56.~~806272~~Z",	21	····················"iopub.status.idle":·"2025-03-18T13:29:18.494405Z",
22	····················"shell.execute_reply":·"2024-02-14T01:38:56.~~80462~~2Z"	22	····················"shell.execute_reply":·"2025-03-18T13:29:18.493332Z"
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 14, 18 lines modified		Offset 14, 18 lines modified
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":·"2024-02-14T01:40:30.~~813~~270Z",	21	····················"iopub.execute_input":·"2025-03-18T13:29:16.942288Z",
22	····················"iopub.status.busy":·"2024-02-14T01:40:30.~~812741~~Z",	22	····················"iopub.status.busy":·"2025-03-18T13:29:16.941917Z",
23	····················"iopub.status.idle":·"2024-02-14T01:40:35.~~352311~~Z",	23	····················"iopub.status.idle":·"2025-03-18T13:29:18.745440Z",
24	····················"shell.execute_reply":·"2024-02-14T01:40:35.~~336268~~Z"	24	····················"shell.execute_reply":·"2025-03-18T13:29:18.744325Z"
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 27, 18 lines modified		Offset 27, 18 lines modified
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":·"2024-02-14T01:39:03.~~877976~~Z",	34	····················"iopub.execute_input":·"2025-03-18T13:29:43.360545Z",
35	····················"iopub.status.busy":·"2024-02-14T01:39:03.~~87742~~7Z",	35	····················"iopub.status.busy":·"2025-03-18T13:29:43.360037Z",
36	····················"iopub.status.idle":·"2024-02-14T01:39:07.31~~2760~~Z",	36	····················"iopub.status.idle":·"2025-03-18T13:29:44.618977Z",
37	····················"shell.execute_reply":·"2024-02-14T01:39:07.~~30555~~3Z"	37	····················"shell.execute_reply":·"2025-03-18T13:29:44.618133Z"
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 244, 15 lines modified		Offset 244, 15 lines modified
244	resp_75·=·res.predict(means75)	244	resp_75·=·res.predict(means75)
245	diff·=·resp_75·-·resp_25	245	diff·=·resp_75·-·resp_25
246	The·interquartile·first·difference·for·the·percentage·of·low·income·households	246	The·interquartile·first·difference·for·the·percentage·of·low·income·households
247	in·a·school·district·is:	247	in·a·school·district·is:
248	[10]:	248	[10]:
249	print("%2.4f%%"·%·(diff*100))	249	print("%2.4f%%"·%·(diff*100))
250	-11.8753%	250	-11.8753%
251	/tmp/ipykernel_645/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single	251	/tmp/ipykernel_5148/4175420381.py:1:·FutureWarning:·Calling·float·on·a·single
252	element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use	252	element·Series·is·deprecated·and·will·raise·a·TypeError·in·the·future.·Use
253	float(ser.iloc[0])·instead	253	float(ser.iloc[0])·instead
254	··print("%2.4f%%"·%·(diff*100))	254	··print("%2.4f%%"·%·(diff*100))
255	\x8\x8\x8\x8·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8¶·\x8\x8\x8\x8	255	\x8\x8\x8\x8·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8¶·\x8\x8\x8\x8
256	We·extract·information·that·will·be·used·to·draw·some·interesting·plots:	256	We·extract·information·that·will·be·used·to·draw·some·interesting·plots:
257	[11]:	257	[11]:
258	nobs·=·res.nobs	258	nobs·=·res.nobs


Offset 8, 34 lines modified		Offset 8, 34 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":·"2024-02-14T01:40:13.~~154155~~Z",	15	····················"iopub.execute_input":·"2025-03-18T13:29:16.993996Z",
16	····················"iopub.status.busy":·"2024-02-14T01:40:13.153~~585~~Z",	16	····················"iopub.status.busy":·"2025-03-18T13:29:16.993620Z",
17	····················"iopub.status.idle":·"2024-02-14T01:40:15.~~048406~~Z",	17	····················"iopub.status.idle":·"2025-03-18T13:29:17.963895Z",
18	····················"shell.execute_reply":·"2024-02-14T01:40:15.~~047~~088Z"	18	····················"shell.execute_reply":·"2025-03-18T13:29:17.963000Z"
19	················}	19	················}
20	············},	20	············},
21	············"outputs":·[],	21	············"outputs":·[],
22	············"source":·[	22	············"source":·[
23	················"%matplotlib·inline"	23	················"%matplotlib·inline"
24	············]	24	············]
25	········},	25	········},
26	········{	26	········{
27	············"cell_type":·"code",	27	············"cell_type":·"code",
28	············"execution_count":·2,	28	············"execution_count":·2,
29	············"metadata":·{	29	············"metadata":·{
30	················"execution":·{	30	················"execution":·{
31	····················"iopub.execute_input":·"2024-02-14T01:40:15.057~~064~~Z",	31	····················"iopub.execute_input":·"2025-03-18T13:29:17.977787Z",
32	····················"iopub.status.busy":·"2024-02-14T01:40:15.~~056417~~Z",	32	····················"iopub.status.busy":·"2025-03-18T13:29:17.977323Z",
33	····················"iopub.status.idle":·"2024-02-14T01:40:18.137805Z",	33	····················"iopub.status.idle":·"2025-03-18T13:29:19.187820Z",
34	····················"shell.execute_reply":·"2024-02-14T01:40:18.136~~276~~Z"	34	····················"shell.execute_reply":·"2025-03-18T13:29:19.186904Z"
35	················}	35	················}
36	············},	36	············},
37	············"outputs":·[],	37	············"outputs":·[],
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",


Offset 486, 17 lines modified		Offset 486, 17 lines modified
486	</pre></div></div>	486	</pre></div></div>
487	</div>	487	</div>
488	<div·class="nboutput·nblast·docutils·container">	488	<div·class="nboutput·nblast·docutils·container">
489	<div·class="prompt·empty·docutils·container">	489	<div·class="prompt·empty·docutils·container">
490	</div>	490	</div>
491	<div·class="output_area·stderr·docutils·container">	491	<div·class="output_area·stderr·docutils·container">
492	<div·class="highlight"><pre>	492	<div·class="highlight"><pre>
493	/tmp/ipykernel_30463/1000445862.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]`	493	/tmp/ipykernel_6302/1000445862.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]`
494	··print(mod1.params[1])	494	··print(mod1.params[1])
495	/tmp/ipykernel_30463/1000445862.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]`	495	/tmp/ipykernel_6302/1000445862.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]`
496	··print(mod2.params[1]·*·2)	496	··print(mod2.params[1]·*·2)
497	</pre></div></div>	497	</pre></div></div>
498	</div>	498	</div>
499	</section>	499	</section>


500	············<div·class="clearer"></div>	500	············<div·class="clearer"></div>


Offset 176, 23 lines modified		Offset 176, 23 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_30463/1000445862.py:1:·FutureWarning:·Series.__getitem__	183	/tmp/ipykernel_6302/1000445862.py:1:·FutureWarning:·Series.__getitem__·treating
184	~~treating·~~keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	184	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always
185	~~will·always·~~be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	185	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by
186	~~access·a·value·by·~~position,·use·`ser.iloc[pos]`	186	position,·use·`ser.iloc[pos]`
187	··print(mod1.params[1])	187	··print(mod1.params[1])
188	/tmp/ipykernel_30463/1000445862.py:2:·FutureWarning:·Series.__getitem__	188	/tmp/ipykernel_6302/1000445862.py:2:·FutureWarning:·Series.__getitem__·treating
189	~~treating·~~keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys	189	keys·as·positions·is·deprecated.·In·a·future·version,·integer·keys·will·always
190	~~will·always·~~be·treated·as·labels·(consistent·with·DataFrame·behavior).·To	190	be·treated·as·labels·(consistent·with·DataFrame·behavior).·To·access·a·value·by
191	~~access·a·value·by·~~position,·use·`ser.iloc[pos]`	191	position,·use·`ser.iloc[pos]`
192	··print(mod2.params[1]·*·2)	192	··print(mod2.params[1]·*·2)
193	_\x8[_\x8L_\x8o_\x8g_\x8o_\x8]	193	_\x8[_\x8L_\x8o_\x8g_\x8o_\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
196	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d	196	····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
197	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e	197	····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
198	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s	198	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\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":·"2024-02-14T01:38:07.~~200758~~Z",	24	····················"iopub.execute_input":·"2025-03-18T13:29:37.489307Z",
25	····················"iopub.status.busy":·"2024-02-14T01:38:07.~~200216~~Z",	25	····················"iopub.status.busy":·"2025-03-18T13:29:37.488937Z",
26	····················"iopub.status.idle":·"2024-02-14T01:38:10.~~012338~~Z",	26	····················"iopub.status.idle":·"2025-03-18T13:29:38.731151Z",
27	····················"shell.execute_reply":·"2024-02-14T01:38:09.~~996256~~Z"	27	····················"shell.execute_reply":·"2025-03-18T13:29:38.730189Z"
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 24, 18 lines modified		Offset 24, 18 lines modified
24	············]	24	············]
25	········},	25	········},
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":·"2024-02-14T01:39:30.~~697841~~Z",	31	····················"iopub.execute_input":·"2025-03-18T13:29:29.828922Z",
32	····················"iopub.status.busy":·"2024-02-14T01:39:30.~~697361~~Z",	32	····················"iopub.status.busy":·"2025-03-18T13:29:29.828529Z",
33	····················"iopub.status.idle":·"2024-02-14T01:39:35.~~224294~~Z",	33	····················"iopub.status.idle":·"2025-03-18T13:29:31.596102Z",
34	····················"shell.execute_reply":·"2024-02-14T01:39:35.~~208~~268Z"	34	····················"shell.execute_reply":·"2025-03-18T13:29:31.595206Z"
35	················}	35	················}
36	············},	36	············},
37	············"outputs":·[],	37	············"outputs":·[],
38	············"source":·[	38	············"source":·[
39	················"%matplotlib·inline\n",	39	················"%matplotlib·inline\n",
40	················"import·numpy·as·np\n",	40	················"import·numpy·as·np\n",
41	················"from·scipy·import·stats\n",	41	················"from·scipy·import·stats\n",


Offset 316, 69 lines modified		Offset 316, 69 lines modified
316	··background:·rgba(66,·165,·245,·0.2);	316	··background:·rgba(66,·165,·245,·0.2);
317	}	317	}
318	</style>	318	</style>
319	<section·id="Mediation-analysis-with-duration-data">	319	<section·id="Mediation-analysis-with-duration-data">
320	<h1>Mediation·analysis·with·duration·data<a·class="headerlink"·href="#Mediation-analysis-with-duration-data"·title="Link·to·this·heading">¶</a></h1>	320	<h1>Mediation·analysis·with·duration·data<a·class="headerlink"·href="#Mediation-analysis-with-duration-data"·title="Link·to·this·heading">¶</a></h1>
321	<p>This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are·duration·variables,·modeled·using·proportional·hazards·regression.·These·examples·are·based·on·simulated·data.</p>	321	<p>This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are·duration·variables,·modeled·using·proportional·hazards·regression.·These·examples·are·based·on·simulated·data.</p>
322	<div·class="nbinput·nblast·docutils·container">	322	<div·class="nbinput·nblast·docutils·container">
323	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:	323	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
324	</pre></div>	324	</pre></div>
325	</div>	325	</div>
326	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>	326	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
327	<span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>	327	<span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
328	<span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>	328	<span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
329	<span·class="kn">from</span>·<span·class="nn">statsmodels.stats.mediation</span>·<span·class="kn">import</span>·<span·class="n">Mediation</span>	329	<span·class="kn">from</span>·<span·class="nn">statsmodels.stats.mediation</span>·<span·class="kn">import</span>·<span·class="n">Mediation</span>
330	</pre></div>	330	</pre></div>
331	</div>	331	</div>
332	</div>	332	</div>
333	<p>Make·the·notebook·reproducible.</p>	333	<p>Make·the·notebook·reproducible.</p>
334	<div·class="nbinput·nblast·docutils·container">	334	<div·class="nbinput·nblast·docutils·container">
335	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:	335	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
336	</pre></div>	336	</pre></div>
337	</div>	337	</div>
338	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3424</span><span·class="p">)</span>	338	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3424</span><span·class="p">)</span>
339	</pre></div>	339	</pre></div>
340	</div>	340	</div>
341	</div>	341	</div>
342	<p>Specify·a·sample·size.</p>	342	<p>Specify·a·sample·size.</p>
343	<div·class="nbinput·nblast·docutils·container">	343	<div·class="nbinput·nblast·docutils·container">
344	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:	344	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
345	</pre></div>	345	</pre></div>
346	</div>	346	</div>
347	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>	347	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>
348	</pre></div>	348	</pre></div>
349	</div>	349	</div>
350	</div>	350	</div>
351	<p>Generate·an·exposure·variable.</p>	351	<p>Generate·an·exposure·variable.</p>
352	<div·class="nbinput·nblast·docutils·container">	352	<div·class="nbinput·nblast·docutils·container">
353	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:	353	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
354	</pre></div>	354	</pre></div>
355	</div>	355	</div>
356	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">exp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>	356	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">exp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>
357	</pre></div>	357	</pre></div>
358	</div>	358	</div>
359	</div>	359	</div>
360	<p>Generate·a·mediator·variable.</p>	360	<p>Generate·a·mediator·variable.</p>
361	<div·class="nbinput·nblast·docutils·container">	361	<div·class="nbinput·nblast·docutils·container">
362	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:	362	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
363	</pre></div>	363	</pre></div>
364	</div>	364	</div>
365	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_mediator</span><span·class="p">():</span>	365	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_mediator</span><span·class="p">():</span>
366	····<span·class="n">mn</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">exp</span><span·class="p">)</span>	366	····<span·class="n">mn</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">exp</span><span·class="p">)</span>
367	····<span·class="n">mtime0</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>	367	····<span·class="n">mtime0</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>
368	····<span·class="n">ctime</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="mi">2</span>·<span·class="o"></span>·<span·class="n">mn</span>·<span·class="o"></span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>	368	····<span·class="n">ctime</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="mi">2</span>·<span·class="o"></span>·<span·class="n">mn</span>·<span·class="o"></span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>
369	····<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">ctime</span>·<span·class="o">>=</span>·<span·class="n">mtime0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>	369	····<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">ctime</span>·<span·class="o">>=</span>·<span·class="n">mtime0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
370	····<span·class="n">mtime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">mtime0</span>·<span·class="o"><=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>	370	····<span·class="n">mtime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">mtime0</span>·<span·class="o"><=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>
371	····<span·class="k">return</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>	371	····<span·class="k">return</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>
372	</pre></div>	372	</pre></div>
373	</div>	373	</div>
374	</div>	374	</div>
375	<p>Generate·an·outcome·variable.</p>	375	<p>Generate·an·outcome·variable.</p>
376	<div·class="nbinput·nblast·docutils·container">	376	<div·class="nbinput·nblast·docutils·container">
377	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:	377	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
378	</pre></div>	378	</pre></div>
379	</div>	379	</div>
380	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">):</span>	380	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">):</span>
381	····<span·class="k">if</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">"full"</span><span·class="p">:</span>	381	····<span·class="k">if</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">"full"</span><span·class="p">:</span>
382	········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>·<span·class="o">*</span>·<span·class="n">mtime0</span>	382	········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>·<span·class="o">*</span>·<span·class="n">mtime0</span>
383	····<span·class="k">elif</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">"no"</span><span·class="p">:</span>	383	····<span·class="k">elif</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">"no"</span><span·class="p">:</span>
384	········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="n">exp</span>	384	········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="n">exp</span>


Offset 6, 68 lines modified		Offset 6, 68 lines modified
6	····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x81_\x8+_\x8d_\x8f_\x8s_\x8g·»	6	····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x81_\x8+_\x8d_\x8f_\x8s_\x8g·»
7	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»	7	····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8	····*·Mediation·analysis·with·duration·data	8	····*·Mediation·analysis·with·duration·data
9	\x8\x8\x8\x8\x8\x8·M\x8Me\x8ed\x8di\x8ia\x8at\x8ti\x8io\x8on\x8n·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s·w\x8wi\x8it\x8th\x8h·d\x8du\x8ur\x8ra\x8at\x8ti\x8io\x8on\x8n·d\x8da\x8at\x8ta\x8a_\x8?\x8¶·\x8\x8\x8\x8\x8\x8	9	\x8\x8\x8\x8\x8\x8·M\x8Me\x8ed\x8di\x8ia\x8at\x8ti\x8io\x8on\x8n·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s·w\x8wi\x8it\x8th\x8h·d\x8du\x8ur\x8ra\x8at\x8ti\x8io\x8on\x8n·d\x8da\x8at\x8ta\x8a_\x8?\x8¶·\x8\x8\x8\x8\x8\x8
10	This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are	10	This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are
11	duration·variables,·modeled·using·proportional·hazards·regression.·These	11	duration·variables,·modeled·using·proportional·hazards·regression.·These
12	examples·are·based·on·simulated·data.	12	examples·are·based·on·simulated·data.
13	[1]:	13	[·]:
14	import·pandas·as·pd	14	import·pandas·as·pd
15	import·numpy·as·np	15	import·numpy·as·np
16	import·statsmodels.api·as·sm	16	import·statsmodels.api·as·sm
17	from·statsmodels.stats.mediation·import·Mediation	17	from·statsmodels.stats.mediation·import·Mediation
18	Make·the·notebook·reproducible.	18	Make·the·notebook·reproducible.
19	[2]:	19	[·]:
20	np.random.seed(3424)	20	np.random.seed(3424)
21	Specify·a·sample·size.	21	Specify·a·sample·size.
22	[3]:	22	[·]:
23	n·=·1000	23	n·=·1000
24	Generate·an·exposure·variable.	24	Generate·an·exposure·variable.
25	[4]:	25	[·]:
26	exp·=·np.random.normal(size=n)	26	exp·=·np.random.normal(size=n)
27	Generate·a·mediator·variable.	27	Generate·a·mediator·variable.
28	[5]:	28	[·]:
29	def·gen_mediator():	29	def·gen_mediator():
30	····mn·=·np.exp(exp)	30	····mn·=·np.exp(exp)
31	····mtime0·=·-mn·*·np.log(np.random.uniform(size=n))	31	····mtime0·=·-mn·*·np.log(np.random.uniform(size=n))
32	····ctime·=·-2··mn··np.log(np.random.uniform(size=n))	32	····ctime·=·-2··mn··np.log(np.random.uniform(size=n))
33	····mstatus·=·(ctime·>=·mtime0).astype(int)	33	····mstatus·=·(ctime·>=·mtime0).astype(int)
34	····mtime·=·np.where(mtime0·<=·ctime,·mtime0,·ctime)	34	····mtime·=·np.where(mtime0·<=·ctime,·mtime0,·ctime)
35	····return·mtime0,·mtime,·mstatus	35	····return·mtime0,·mtime,·mstatus
36	Generate·an·outcome·variable.	36	Generate·an·outcome·variable.
37	[6]:	37	[·]:
38	def·gen_outcome(otype,·mtime0):	38	def·gen_outcome(otype,·mtime0):
39	····if·otype·==·"full":	39	····if·otype·==·"full":
40	········lp·=·0.5·*·mtime0	40	········lp·=·0.5·*·mtime0
41	····elif·otype·==·"no":	41	····elif·otype·==·"no":
42	········lp·=·exp	42	········lp·=·exp
43	····else:	43	····else:
44	········lp·=·exp·+·mtime0	44	········lp·=·exp·+·mtime0
45	····mn·=·np.exp(-lp)	45	····mn·=·np.exp(-lp)
46	····ytime0·=·-mn·*·np.log(np.random.uniform(size=n))	46	····ytime0·=·-mn·*·np.log(np.random.uniform(size=n))
47	····ctime·=·-2··mn··np.log(np.random.uniform(size=n))	47	····ctime·=·-2··mn··np.log(np.random.uniform(size=n))
48	····ystatus·=·(ctime·>=·ytime0).astype(int)	48	····ystatus·=·(ctime·>=·ytime0).astype(int)
49	····ytime·=·np.where(ytime0·<=·ctime,·ytime0,·ctime)	49	····ytime·=·np.where(ytime0·<=·ctime,·ytime0,·ctime)
50	····return·ytime,·ystatus	50	····return·ytime,·ystatus
51	Build·a·dataframe·containing·all·the·relevant·variables.	51	Build·a·dataframe·containing·all·the·relevant·variables.
52	[7]:	52	[·]:
53	def·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus):	53	def·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus):
54	····df·=·pd.DataFrame(	54	····df·=·pd.DataFrame(
55	········{	55	········{
56	············"ytime":·ytime,	56	············"ytime":·ytime,
57	············"ystatus":·ystatus,	57	············"ystatus":·ystatus,
58	············"mtime":·mtime,	58	············"mtime":·mtime,
59	············"mstatus":·mstatus,	59	············"mstatus":·mstatus,
60	············"exp":·exp,	60	············"exp":·exp,
61	········}	61	········}
62	····)	62	····)
63	····return·df	63	····return·df
64	Run·the·full·simulation·and·analysis,·under·a·particular·population·structure	64	Run·the·full·simulation·and·analysis,·under·a·particular·population·structure
65	of·mediation.	65	of·mediation.
66	[8]:	66	[·]:
67	def·run(otype):	67	def·run(otype):

68	····mtime0,·mtime,·mstatus·=·gen_mediator()	68	····mtime0,·mtime,·mstatus·=·gen_mediator()
69	····ytime,·ystatus·=·gen_outcome(otype,·mtime0)	69	····ytime,·ystatus·=·gen_outcome(otype,·mtime0)
70	····df·=·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus)	70	····df·=·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus)

71	····outcome_model·=·sm.PHReg.from_formula(	71	····outcome_model·=·sm.PHReg.from_formula(


Offset 24, 34 lines modified		Offset 24, 34 lines modified
24	············]	24	············]
25	········},	25	········},
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":·"2024-02-14T01:38:07.~~885993~~Z",	31	····················"iopub.execute_input":·"2025-03-18T13:29:30.638660Z",
32	····················"iopub.status.busy":·"2024-02-14T01:38:0~~7.8~~85503Z",	32	····················"iopub.status.busy":·"2025-03-18T13:29:30.638258Z",
33	····················"iopub.status.idle":·"2024-02-14T01:38:09.936301Z",	33	····················"iopub.status.idle":·"2025-03-18T13:29:31.337634Z",
34	····················"shell.execute_reply":·"2024-02-14T01:38:09.~~920260~~Z"	34	····················"shell.execute_reply":·"2025-03-18T13:29:31.336755Z"
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":·"2024-02-14T01:38:09.~~958129~~Z",	47	····················"iopub.execute_input":·"2025-03-18T13:29:31.342681Z",
48	····················"iopub.status.busy":·"2024-02-14T01:38:09.~~957491~~Z",	48	····················"iopub.status.busy":·"2025-03-18T13:29:31.342227Z",
49	····················"iopub.status.idle":·"2024-02-14T01:38:11.~~993538~~Z",	49	····················"iopub.status.idle":·"2025-03-18T13:29:32.210394Z",
50	····················"shell.execute_reply":·"2024-02-14T01:38:11.~~992~~321Z"	50	····················"shell.execute_reply":·"2025-03-18T13:29:32.209325Z"
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 705, 23 lines modified		Offset 705, 14 lines modified
705	<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>	705	<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>
706	</pre></div>	706	</pre></div>
707	</div>	707	</div>
708	</div>	708	</div>
709	<div·class="nboutput·docutils·container">	709	<div·class="nboutput·docutils·container">
710	<div·class="prompt·empty·docutils·container">	710	<div·class="prompt·empty·docutils·container">
711	</div>	711	</div>
712	<div·class="output_area·stderr·docutils·container">
713	<div·class="highlight"><pre>
714	/usr/lib/python3/dist-packages/statsmodels/regression/mixed_linear_model.py:2238:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter·space.
715	··warnings.warn(msg,·ConvergenceWarning)
716	</pre></div></div>
717	</div>
718	<div·class="nboutput·nblast·docutils·container">
719	<div·class="prompt·empty·docutils·container">
720	</div>
721	<div·class="output_area·docutils·container">	712	<div·class="output_area·docutils·container">
722	<div·class="highlight"><pre>	713	<div·class="highlight"><pre>
723	·············Mixed·Linear·Model·Regression·Results	714	·············Mixed·Linear·Model·Regression·Results
724	===============================================================	715	===============================================================
725	Model:···············MixedLM····Dependent·Variable:····size	716	Model:···············MixedLM····Dependent·Variable:····size
726	No.·Observations:····395········Method:················REML	717	No.·Observations:····395········Method:················REML
727	No.·Groups:··········79·········Scale:·················0.0264	718	No.·Groups:··········79·········Scale:·················0.0264


Offset 316, 18 lines modified		Offset 316, 14 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	2238:·ConvergenceWarning:·The·MLE·may·be·on·the·boundary·of·the·parameter
325	space.
326	··warnings.warn(msg,·ConvergenceWarning)
327	·············Mixed·Linear·Model·Regression·Results	323	·············Mixed·Linear·Model·Regression·Results
328	===============================================================	324	===============================================================
329	Model:···············MixedLM····Dependent·Variable:····size	325	Model:···············MixedLM····Dependent·Variable:····size
330	No.·Observations:····395········Method:················REML	326	No.·Observations:····395········Method:················REML
331	No.·Groups:··········79·········Scale:·················0.0264	327	No.·Groups:··········79·········Scale:·················0.0264
332	Min.·group·size:·····5··········Log-Likelihood:········-62.4834	328	Min.·group·size:·····5··········Log-Likelihood:········-62.4834
333	Max.·group·size:·····5··········Converged:·············Yes	329	Max.·group·size:·····5··········Converged:·············Yes


Offset 799, 15 lines modified		Offset 799, 15 lines modified
799	</div>	799	</div>
800	</div>	800	</div>
801	<div·class="nboutput·docutils·container">	801	<div·class="nboutput·docutils·container">
802	<div·class="prompt·empty·docutils·container">	802	<div·class="prompt·empty·docutils·container">
803	</div>	803	</div>
804	<div·class="output_area·stderr·docutils·container">	804	<div·class="output_area·stderr·docutils·container">
805	<div·class="highlight"><pre>	805	<div·class="highlight"><pre>
806	/tmp/ipykernel_~~382~~/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be·used·together·with·FixedLocator	806	/tmp/ipykernel_6296/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be·used·together·with·FixedLocator
807	··ax.set_xticklabels(dta.columns.values[::10])	807	··ax.set_xticklabels(dta.columns.values[::10])
808	</pre></div></div>	808	</pre></div></div>
809	</div>	809	</div>
810	<div·class="nboutput·nblast·docutils·container">	810	<div·class="nboutput·nblast·docutils·container">
811	<div·class="prompt·empty·docutils·container">	811	<div·class="prompt·empty·docutils·container">
812	</div>	812	</div>
813	<div·class="output_area·docutils·container">	813	<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_~~382~~/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be	133	/tmp/ipykernel_6296/427128218.py:3:·UserWarning:·FixedFormatter·should·only·be
134	used·together·with·FixedLocator	134	used·together·with·FixedLocator
135	··ax.set_xticklabels(dta.columns.values[::10])	135	··ax.set_xticklabels(dta.columns.values[::10])
136	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]	136	[../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png]
137	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories	137	To·better·understand·what·is·going·on,·we·will·plot·the·fertility·trajectories
138	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience	138	for·sets·of·countries·with·similar·PC·scores.·The·following·convenience
139	function·produces·such·a·plot.	139	function·produces·such·a·plot.
140	[8]:	140	[8]:


Offset 42, 18 lines modified		Offset 42, 18 lines modified
42	········},	42	········},
43	········{	43	········{
44	············"cell_type":·"code",	44	············"cell_type":·"code",
45	············"execution_count":·1,	45	············"execution_count":·1,
46	············"id":·"3f9f42c9",	46	············"id":·"3f9f42c9",
47	············"metadata":·{	47	············"metadata":·{
48	················"execution":·{	48	················"execution":·{
49	····················"iopub.execute_input":·"2024-02-14T01:40:25.690~~077~~Z",	49	····················"iopub.execute_input":·"2025-03-18T13:29:28.190132Z",
50	····················"iopub.status.busy":·"2024-02-14T01:40:25.689~~469~~Z",	50	····················"iopub.status.busy":·"2025-03-18T13:29:28.189703Z",
51	····················"iopub.status.idle":·"2024-02-14T01:40:29.~~400298~~Z",	51	····················"iopub.status.idle":·"2025-03-18T13:29:29.655300Z",
52	····················"shell.execute_reply":·"2024-02-14T01:40:29.~~388276~~Z"	52	····················"shell.execute_reply":·"2025-03-18T13:29:29.654381Z"
53	················}	53	················}
54	············},	54	············},
55	············"outputs":·[],	55	············"outputs":·[],
56	············"source":·[	56	············"source":·[
57	················"import·numpy·as·np\n",	57	················"import·numpy·as·np\n",
58	················"import·pandas·as·pd\n",	58	················"import·pandas·as·pd\n",
59	················"from·scipy·import·stats\n",	59	················"from·scipy·import·stats\n",


Offset 2055, 15 lines modified		Offset 2055, 15 lines modified
2055	</div>	2055	</div>
2056	<div·class="nboutput·nblast·docutils·container">	2056	<div·class="nboutput·nblast·docutils·container">
2057	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[67]:	2057	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[67]:
2058	</pre></div>	2058	</pre></div>
2059	</div>	2059	</div>
2060	<div·class="output_area·docutils·container">	2060	<div·class="output_area·docutils·container">
2061	<div·class="highlight"><pre>	2061	<div·class="highlight"><pre>
2062	0.4450294873068328	2062	0.4450294873068327
2063	</pre></div></div>	2063	</pre></div></div>
2064	</div>	2064	</div>
2065	<div·class="nbinput·docutils·container">	2065	<div·class="nbinput·docutils·container">
2066	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[68]:	2066	<div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[68]:
2067	</pre></div>	2067	</pre></div>
2068	</div>	2068	</div>
2069	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">all_betas</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">)</span>	2069	<div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">all_betas</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">)</span>


Offset 890, 15 lines modified		Offset 890, 15 lines modified
890	all_betas·=·np.asarray(all_betas)	890	all_betas·=·np.asarray(all_betas)
891	se_loss·=·lambda·x:·np.linalg.norm(x,·ord=2)·**·2	891	se_loss·=·lambda·x:·np.linalg.norm(x,·ord=2)·**·2
892	se_beta·=·lmap(se_loss,·all_betas·-·beta_true)	892	se_beta·=·lmap(se_loss,·all_betas·-·beta_true)
893	\x8\x8\x8\x8·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8ed\x8d·e\x8er\x8rr\x8ro\x8or\x8r·l\x8lo\x8os\x8ss\x8s_\x8?\x8¶·\x8\x8\x8\x8	893	\x8\x8\x8\x8·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8ed\x8d·e\x8er\x8rr\x8ro\x8or\x8r·l\x8lo\x8os\x8ss\x8s_\x8?\x8¶·\x8\x8\x8\x8
894	[67]:	894	[67]:
895	np.array(se_beta).mean()	895	np.array(se_beta).mean()
896	[67]:	896	[67]:
897	0.4450294873068328	897	0.4450294873068327
898	[68]:	898	[68]:
899	all_betas.mean(0)	899	all_betas.mean(0)
900	[68]:	900	[68]:
901	array([·2.99711706,··0.99898147,··2.49909344,··2.99712918,·-3.99626521])	901	array([·2.99711706,··0.99898147,··2.49909344,··2.99712918,·-3.99626521])
902	[69]:	902	[69]:
903	beta_true	903	beta_true
904	[69]:	904	[69]: