Discrete Choice Models Overview ================================= .. _discrete_choice_overview_notebook: `Link to Notebook GitHub <https://github.com/statsmodels/statsmodels/blob/master/examples/notebooks/discrete_choice_overview.ipynb>`_ .. raw:: html <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">statsmodels.api</span> <span class="k">as</span> <span class="nn">sm</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Data">Data<a class="anchor-link" href="#Data">¶</a></h2><p>Load data from Spector and Mazzeo (1980). Examples follow Greene's Econometric Analysis Ch. 21 (5th Edition).</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">spector_data</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">spector</span><span class="o">.</span><span class="n">load</span><span class="p">()</span> <span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">,</span> <span class="n">prepend</span><span class="o">=</span><span class="k">False</span><span class="p">)</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Inspect the data:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="nb">print</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">[:</span><span class="mi">5</span><span class="p">,:])</span> <span class="nb">print</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">endog</span><span class="p">[:</span><span class="mi">5</span><span class="p">])</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Linear-Probability-Model-(OLS)">Linear Probability Model (OLS)<a class="anchor-link" href="#Linear-Probability-Model-(OLS)">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">lpm_mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">OLS</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">)</span> <span class="n">lpm_res</span> <span class="o">=</span> <span class="n">lpm_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> <span class="nb">print</span><span class="p">(</span><span class="s">'Parameters: '</span><span class="p">,</span> <span class="n">lpm_res</span><span class="o">.</span><span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>[[ 2.66 20. 0. 1. ] [ 2.89 22. 0. 1. ] [ 3.28 24. 0. 1. ] [ 2.92 12. 0. 1. ] [ 4. 21. 0. 1. ]] [ 0. 0. 0. 0. 1.] </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Logit-Model">Logit Model<a class="anchor-link" href="#Logit-Model">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">logit_mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">Logit</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">)</span> <span class="n">logit_res</span> <span class="o">=</span> <span class="n">logit_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">disp</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="s">'Parameters: '</span><span class="p">,</span> <span class="n">logit_res</span><span class="o">.</span><span class="n">params</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Parameters: [ 0.46385168 0.01049512 0.37855479] </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Marginal Effects</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">margeff</span> <span class="o">=</span> <span class="n">logit_res</span><span class="o">.</span><span class="n">get_margeff</span><span class="p">()</span> <span class="nb">print</span><span class="p">(</span><span class="n">margeff</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Parameters: [ 2.82611259 0.09515766 2.37868766 -13.02134686] </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>As in all the discrete data models presented below, we can print a nice summary of results:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="nb">print</span><span class="p">(</span><span class="n">logit_res</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre> Logit Marginal Effects ===================================== Dep. Variable: y Method: dydx At: overall ============================================================================== dy/dx std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 0.3626 0.109 3.313 0.001 0.148 0.577 x2 0.0122 0.018 0.686 0.493 -0.023 0.047 x3 0.3052 0.092 3.304 0.001 0.124 0.486 ============================================================================== </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Probit-Model">Probit Model<a class="anchor-link" href="#Probit-Model">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">probit_mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">Probit</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">)</span> <span class="n">probit_res</span> <span class="o">=</span> <span class="n">probit_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> <span class="n">probit_margeff</span> <span class="o">=</span> <span class="n">probit_res</span><span class="o">.</span><span class="n">get_margeff</span><span class="p">()</span> <span class="nb">print</span><span class="p">(</span><span class="s">'Parameters: '</span><span class="p">,</span> <span class="n">probit_res</span><span class="o">.</span><span class="n">params</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="s">'Marginal effects: '</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="n">probit_margeff</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre> Logit Regression Results ============================================================================== Dep. Variable: y No. Observations: 32 Model: Logit Df Residuals: 28 Method: MLE Df Model: 3 Date: Mon, 20 Jul 2015 Pseudo R-squ.: 0.3740 Time: 17:43:21 Log-Likelihood: -12.890 converged: True LL-Null: -20.592 LLR p-value: 0.001502 ============================================================================== coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 2.8261 1.263 2.238 0.025 0.351 5.301 x2 0.0952 0.142 0.672 0.501 -0.182 0.373 x3 2.3787 1.065 2.234 0.025 0.292 4.465 const -13.0213 4.931 -2.641 0.008 -22.687 -3.356 ============================================================================== </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Multinomial-Logit">Multinomial Logit<a class="anchor-link" href="#Multinomial-Logit">¶</a></h2> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Load data from the American National Election Studies:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">anes_data</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">anes96</span><span class="o">.</span><span class="n">load</span><span class="p">()</span> <span class="n">anes_exog</span> <span class="o">=</span> <span class="n">anes_data</span><span class="o">.</span><span class="n">exog</span> <span class="n">anes_exog</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">anes_exog</span><span class="p">,</span> <span class="n">prepend</span><span class="o">=</span><span class="k">False</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Optimization terminated successfully. Current function value: 0.400588 Iterations 6 Parameters: [ 1.62581004 0.05172895 1.42633234 -7.45231965] Marginal effects: Probit Marginal Effects ===================================== Dep. Variable: y Method: dydx At: overall ============================================================================== dy/dx std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 0.3608 0.113 3.182 0.001 0.139 0.583 x2 0.0115 0.018 0.624 0.533 -0.025 0.048 x3 0.3165 0.090 3.508 0.000 0.140 0.493 ============================================================================== </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Inspect the data:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="nb">print</span><span class="p">(</span><span class="n">anes_data</span><span class="o">.</span><span class="n">exog</span><span class="p">[:</span><span class="mi">5</span><span class="p">,:])</span> <span class="nb">print</span><span class="p">(</span><span class="n">anes_data</span><span class="o">.</span><span class="n">endog</span><span class="p">[:</span><span class="mi">5</span><span class="p">])</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Fit MNL model:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">mlogit_mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">MNLogit</span><span class="p">(</span><span class="n">anes_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">anes_exog</span><span class="p">)</span> <span class="n">mlogit_res</span> <span class="o">=</span> <span class="n">mlogit_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span> <span class="nb">print</span><span class="p">(</span><span class="n">mlogit_res</span><span class="o">.</span><span class="n">params</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>[[ -2.30258509 7. 36. 3. 1. ] [ 5.24755025 3. 20. 4. 1. ] [ 3.43720782 2. 24. 6. 1. ] [ 4.4200447 3. 28. 6. 1. ] [ 6.46162441 5. 68. 6. 1. ]] [ 6. 1. 1. 1. 0.] </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Poisson">Poisson<a class="anchor-link" href="#Poisson">¶</a></h2><p>Load the Rand data. Note that this example is similar to Cameron and Trivedi's <code>Microeconometrics</code> Table 20.5, but it is slightly different because of minor changes in the data.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">rand_data</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">randhie</span><span class="o">.</span><span class="n">load</span><span class="p">()</span> <span class="n">rand_exog</span> <span class="o">=</span> <span class="n">rand_data</span><span class="o">.</span><span class="n">exog</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rand_data</span><span class="o">.</span><span class="n">exog</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="n">rand_exog</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">rand_exog</span><span class="p">,</span> <span class="n">prepend</span><span class="o">=</span><span class="k">False</span><span class="p">)</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Optimization terminated successfully. Current function value: 1.548647 Iterations 7 [[ -1.15359746e-02 -8.87506530e-02 -1.05966699e-01 -9.15567017e-02 -9.32846040e-02 -1.40880692e-01] [ 2.97714352e-01 3.91668642e-01 5.73450508e-01 1.27877179e+00 1.34696165e+00 2.07008014e+00] [ -2.49449954e-02 -2.28978371e-02 -1.48512069e-02 -8.68134503e-03 -1.79040689e-02 -9.43264870e-03] [ 8.24914421e-02 1.81042758e-01 -7.15241904e-03 1.99827955e-01 2.16938850e-01 3.21925702e-01] [ 5.19655317e-03 4.78739761e-02 5.75751595e-02 8.44983753e-02 8.09584122e-02 1.08894083e-01] [ -3.73401677e-01 -2.25091318e+00 -3.66558353e+00 -7.61384309e+00 -7.06047825e+00 -1.21057509e+01]] </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <p>Fit Poisson model:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">poisson_mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">Poisson</span><span class="p">(</span><span class="n">rand_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">rand_exog</span><span class="p">)</span> <span class="n">poisson_res</span> <span class="o">=</span> <span class="n">poisson_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s">"newton"</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="n">poisson_res</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Negative-Binomial">Negative Binomial<a class="anchor-link" href="#Negative-Binomial">¶</a></h2><p>The negative binomial model gives slightly different results.</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">mod_nbin</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">NegativeBinomial</span><span class="p">(</span><span class="n">rand_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">rand_exog</span><span class="p">)</span> <span class="n">res_nbin</span> <span class="o">=</span> <span class="n">mod_nbin</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">disp</span><span class="o">=</span><span class="k">False</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="n">res_nbin</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre>Optimization terminated successfully. Current function value: 3.091609 Iterations 12 Poisson Regression Results ============================================================================== Dep. Variable: y No. Observations: 20190 Model: Poisson Df Residuals: 20180 Method: MLE Df Model: 9 Date: Mon, 20 Jul 2015 Pseudo R-squ.: 0.06343 Time: 17:43:22 Log-Likelihood: -62420. converged: True LL-Null: -66647. LLR p-value: 0.000 ============================================================================== coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0525 0.003 -18.216 0.000 -0.058 -0.047 x2 -0.2471 0.011 -23.272 0.000 -0.268 -0.226 x3 0.0353 0.002 19.302 0.000 0.032 0.039 x4 -0.0346 0.002 -21.439 0.000 -0.038 -0.031 x5 0.2717 0.012 22.200 0.000 0.248 0.296 x6 0.0339 0.001 60.098 0.000 0.033 0.035 x7 -0.0126 0.009 -1.366 0.172 -0.031 0.005 x8 0.0541 0.015 3.531 0.000 0.024 0.084 x9 0.2061 0.026 7.843 0.000 0.155 0.258 const 0.7004 0.011 62.741 0.000 0.678 0.722 ============================================================================== </pre> </div> </div> </div> </div> </div> <div class="cell border-box-sizing text_cell rendered"> <div class="prompt input_prompt"> </div> <div class="inner_cell"> <div class="text_cell_render border-box-sizing rendered_html"> <h2 id="Alternative-solvers">Alternative solvers<a class="anchor-link" href="#Alternative-solvers">¶</a></h2><p>The default method for fitting discrete data MLE models is Newton-Raphson. You can use other solvers by using the <code>method</code> argument:</p> </div> </div> </div> <div class="cell border-box-sizing code_cell rendered"> <div class="input"> <div class="prompt input_prompt">In [ ]:</div> <div class="inner_cell"> <div class="input_area"> <div class=" highlight hl-ipython3"><pre><span class="n">mlogit_res</span> <span class="o">=</span> <span class="n">mlogit_mod</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s">'bfgs'</span><span class="p">,</span> <span class="n">maxiter</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span> <span class="nb">print</span><span class="p">(</span><span class="n">mlogit_res</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span> </pre></div> </div> </div> </div> <div class="output_wrapper"> <div class="output"> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stdout output_text"> <pre> NegativeBinomial Regression Results ============================================================================== Dep. Variable: y No. Observations: 20190 Model: NegativeBinomial Df Residuals: 20180 Method: MLE Df Model: 9 Date: Mon, 20 Jul 2015 Pseudo R-squ.: 0.01845 Time: 17:43:23 Log-Likelihood: -43384. converged: False LL-Null: -44199. LLR p-value: 0.000 ============================================================================== coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0580 0.006 -9.517 0.000 -0.070 -0.046 x2 -0.2678 0.023 -11.802 0.000 -0.312 -0.223 x3 0.0412 0.004 9.937 0.000 0.033 0.049 x4 -0.0381 0.003 -11.219 0.000 -0.045 -0.031 x5 0.2690 0.030 8.981 0.000 0.210 0.328 x6 0.0382 0.001 26.081 0.000 0.035 0.041 x7 -0.0441 0.020 -2.200 0.028 -0.083 -0.005 x8 0.0172 0.036 0.477 0.633 -0.054 0.088 x9 0.1780 0.074 2.397 0.017 0.032 0.324 const 0.6636 0.025 26.787 0.000 0.615 0.712 alpha 1.2930 0.019 69.477 0.000 1.256 1.329 ============================================================================== </pre> </div> </div> <div class="output_area"><div class="prompt"></div> <div class="output_subarea output_stream output_stderr output_text"> <pre>/Users/tom.augspurger/Envs/py3/lib/python3.4/site-packages/statsmodels-0.6.1-py3.4-macosx-10.10-x86_64.egg/statsmodels/base/model.py:466: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals "Check mle_retvals", ConvergenceWarning) </pre> </div> </div> </div> </div> </div> <script src="https://c328740.ssl.cf1.rackcdn.com/mathjax/latest/MathJax.js?config=TeX-AMS_HTML"type="text/javascript"></script> <script type="text/javascript"> init_mathjax = function() { if (window.MathJax) { // MathJax loaded MathJax.Hub.Config({ tex2jax: { // I'm not sure about the \( and \[ below. It messes with the // prompt, and I think it's an issue with the template. -SS inlineMath: [ ['$','$'], ["\\(","\\)"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ] }, displayAlign: 'left', // Change this to 'center' to center equations. "HTML-CSS": { styles: {'.MathJax_Display': {"margin": 0}} } }); MathJax.Hub.Queue(["Typeset",MathJax.Hub]); } } init_mathjax(); // since we have to load this in a ..raw:: directive we will add the css // after the fact function loadcssfile(filename){ var fileref=document.createElement("link") fileref.setAttribute("rel", "stylesheet") fileref.setAttribute("type", "text/css") fileref.setAttribute("href", filename) document.getElementsByTagName("head")[0].appendChild(fileref) } // loadcssfile({{pathto("_static/nbviewer.pygments.css", 1) }}) // loadcssfile({{pathto("_static/nbviewer.min.css", 1) }}) loadcssfile("../../../_static/nbviewer.pygments.css") loadcssfile("../../../_static/ipython.min.css") </script>