Generalized Linear Models (Formula)
This notebook illustrates how you can use R-style formulas to fit Generalized Linear Models.
To begin, we load the Star98 dataset and we construct a formula and pre-process the data:
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1 2 3 4 5 6 7 8 9 10 11 12 | <span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">print_function</span><span class="kn">import</span> <span class="nn">statsmodels.api</span> <span class="kn">as</span> <span class="nn">sm</span><span class="kn">import</span> <span class="nn">statsmodels.formula.api</span> <span class="kn">as</span> <span class="nn">smf</span><span class="n">star98</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">star98</span><span class="o">.</span><span class="n">load_pandas</span><span class="p">()</span><span class="o">.</span><span class="n">data</span><span class="n">formula</span> <span class="o">=</span> <span class="s">'SUCCESS ~ LOWINC + PERASIAN + PERBLACK + PERHISP + PCTCHRT + </span><span class="se">\</span><span class="s"> PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'</span><span class="n">dta</span> <span class="o">=</span> <span class="n">star98</span><span class="p">[[</span><span class="s">'NABOVE'</span><span class="p">,</span> <span class="s">'NBELOW'</span><span class="p">,</span> <span class="s">'LOWINC'</span><span class="p">,</span> <span class="s">'PERASIAN'</span><span class="p">,</span> <span class="s">'PERBLACK'</span><span class="p">,</span> <span class="s">'PERHISP'</span><span class="p">,</span> <span class="s">'PCTCHRT'</span><span class="p">,</span> <span class="s">'PCTYRRND'</span><span class="p">,</span> <span class="s">'PERMINTE'</span><span class="p">,</span> <span class="s">'AVYRSEXP'</span><span class="p">,</span> <span class="s">'AVSALK'</span><span class="p">,</span> <span class="s">'PERSPENK'</span><span class="p">,</span> <span class="s">'PTRATIO'</span><span class="p">,</span> <span class="s">'PCTAF'</span><span class="p">]]</span><span class="n">endog</span> <span class="o">=</span> <span class="n">dta</span><span class="p">[</span><span class="s">'NABOVE'</span><span class="p">]</span> <span class="o">/</span> <span class="p">(</span><span class="n">dta</span><span class="p">[</span><span class="s">'NABOVE'</span><span class="p">]</span> <span class="o">+</span> <span class="n">dta</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="s">'NBELOW'</span><span class="p">))</span><span class="k">del</span> <span class="n">dta</span><span class="p">[</span><span class="s">'NABOVE'</span><span class="p">]</span><span class="n">dta</span><span class="p">[</span><span class="s">'SUCCESS'</span><span class="p">]</span> <span class="o">=</span> <span class="n">endog</span> |
Then, we fit the GLM model:
In [2]:
1 2 | <span class="n">mod1</span> <span class="o">=</span> <span class="n">smf</span><span class="o">.</span><span class="n">glm</span><span class="p">(</span><span class="n">formula</span><span class="o">=</span><span class="n">formula</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">dta</span><span class="p">,</span> <span class="n">family</span><span class="o">=</span><span class="n">sm</span><span class="o">.</span><span class="n">families</span><span class="o">.</span><span class="n">Binomial</span><span class="p">())</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span><span class="n">mod1</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span> |
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Finally, we define a function to operate customized data transformation using the formula framework:
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1 2 3 4 5 6 | <span class="k">def</span> <span class="nf">double_it</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">x</span><span class="n">formula</span> <span class="o">=</span> <span class="s">'SUCCESS ~ double_it(LOWINC) + PERASIAN + PERBLACK + PERHISP + PCTCHRT + </span><span class="se">\</span><span class="s"> PCTYRRND + PERMINTE*AVYRSEXP*AVSALK + PERSPENK*PTRATIO*PCTAF'</span><span class="n">mod2</span> <span class="o">=</span> <span class="n">smf</span><span class="o">.</span><span class="n">glm</span><span class="p">(</span><span class="n">formula</span><span class="o">=</span><span class="n">formula</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">dta</span><span class="p">,</span> <span class="n">family</span><span class="o">=</span><span class="n">sm</span><span class="o">.</span><span class="n">families</span><span class="o">.</span><span class="n">Binomial</span><span class="p">())</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span><span class="n">mod2</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span> |
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As expected, the coefficient for double_it(LOWINC) in the second model is half the size of the LOWINC coefficient from the first model:
In [4]:
1 2 | <span class="k">print</span><span class="p">(</span><span class="n">mod1</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="k">print</span><span class="p">(</span><span class="n">mod2</span><span class="o">.</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span> |
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