notebook.community

Edit and run 





In [1]:



    


%pylab inline
import pandas as pd



    


















    






Populating the interactive namespace from numpy and matplotlib

Logistic Regression = Binomial regression with logit function

This notebook shows (empirically) that performing a logistic regression for binary data is equivalent to a binomial regression with logit link.





In [23]:



    


ungrouped_data = pd.read_csv("../data/Beetles.dat", sep="\t")
ungrouped_data



    


















    
Out[23]:











  
    

      
      x
      y
    

  
  
    

      0
      1.691
      1
    

    

      1
      1.691
      1
    

    

      2
      1.691
      1
    

    

      3
      1.691
      1
    

    

      4
      1.691
      1
    

    

      ...
      ...
      ...
    

    

      476
      1.884
      1
    

    

      477
      1.884
      1
    

    

      478
      1.884
      1
    

    

      479
      1.884
      1
    

    

      480
      1.884
      1
    

  



481 rows × 2 columns



















In [34]:



    


grouped_data = pd.read_csv("../data/Beetles2.dat", sep= "\t")
grouped_data['alive'] = grouped_data['n'] - grouped_data['dead']
grouped_data



    


















    
Out[34]:











  
    

      
      logdose
      n
      dead
      alive
    

  
  
    

      0
      1.691
      59
      6
      53
    

    

      1
      1.724
      60
      13
      47
    

    

      2
      1.755
      62
      18
      44
    

    

      3
      1.784
      56
      28
      28
    

    

      4
      1.811
      63
      52
      11
    

    

      5
      1.837
      59
      53
      6
    

    

      6
      1.861
      62
      61
      1
    

    

      7
      1.884
      60
      60
      0

Logistic





In [25]:



    


import statsmodels.api as sm
#spector_data.exog = sm.add_constant(spector_data.exog)
logit_mod = sm.Logit(ungrouped_data['y'], sm.add_constant(ungrouped_data['x']))
logit_res = logit_mod.fit()



    


















    






Optimization terminated successfully.
         Current function value: 0.387063
         Iterations 7

















In [26]:



    


print(logit_res.summary())



    


















    






                           Logit Regression Results                           
==============================================================================
Dep. Variable:                      y   No. Observations:                  481
Model:                          Logit   Df Residuals:                      479
Method:                           MLE   Df Model:                            1
Date:                Fri, 07 Feb 2020   Pseudo R-squ.:                  0.4231
Time:                        16:09:36   Log-Likelihood:                -186.18
converged:                       True   LL-Null:                       -322.72
Covariance Type:            nonrobust   LLR p-value:                 2.411e-61
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const        -60.7401      5.182    -11.722      0.000     -70.896     -50.584
x             34.2859      2.913     11.769      0.000      28.576      39.996
==============================================================================

Binomial





In [27]:



    


glm_model = sm.GLM(grouped_data['dead']/grouped_data['n'], sm.add_constant(grouped_data['logdose']), family=sm.families.Binomial(link=sm.families.links.logit),
                   weights = grouped_data['n'])
glm_fit = glm_model.fit()
print(glm_fit.summary())



    


















    






                 Generalized Linear Model Regression Results                  
==============================================================================
Dep. Variable:                      y   No. Observations:                    8
Model:                            GLM   Df Residuals:                        6
Model Family:                Binomial   Df Model:                            1
Link Function:                  logit   Scale:                          1.0000
Method:                          IRLS   Log-Likelihood:                -2.1699
Date:                Fri, 07 Feb 2020   Deviance:                      0.18673
Time:                        16:09:58   Pearson chi2:                    0.166
No. Iterations:                     5                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const        -60.4819     40.062     -1.510      0.131    -139.002      18.039
logdose       34.1370     22.522      1.516      0.130     -10.005      78.279
==============================================================================










    






/home/cmb-06/as/skchoudh/software_frozen/anaconda37/envs/riboraptor/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.
Use an instance of a link class instead.
  """Entry point for launching an IPython kernel.

The above is an abuse of statsmodels. I don't even know why it works.





In [35]:



    


glm_model = sm.GLM(grouped_data[['dead', 'alive']] , sm.add_constant(grouped_data['logdose']), family=sm.families.Binomial(link=sm.families.links.logit),
                   )
glm_fit = glm_model.fit()
print(glm_fit.summary())



    


















    






                 Generalized Linear Model Regression Results                  
==============================================================================
Dep. Variable:      ['dead', 'alive']   No. Observations:                    8
Model:                            GLM   Df Residuals:                        6
Model Family:                Binomial   Df Model:                            1
Link Function:                  logit   Scale:                          1.0000
Method:                          IRLS   Log-Likelihood:                -18.657
Date:                Fri, 07 Feb 2020   Deviance:                       11.116
Time:                        17:25:29   Pearson chi2:                     9.91
No. Iterations:                     6                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const        -60.7401      5.182    -11.722      0.000     -70.896     -50.584
logdose       34.2859      2.913     11.769      0.000      28.576      39.996
==============================================================================










    






/home/cmb-06/as/skchoudh/software_frozen/anaconda37/envs/riboraptor/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.
Use an instance of a link class instead.
  """Entry point for launching an IPython kernel.

















In [16]:



    


glm_model = sm.GLM(grouped_data['y'], sm.add_constant(grouped_data['x']), family=sm.families.Binomial(link=sm.families.links.logit))
glm_fit = glm_model.fit()
print(glm_fit.summary())



    


















    






                 Generalized Linear Model Regression Results                  
==============================================================================
Dep. Variable:                      y   No. Observations:                  481
Model:                            GLM   Df Residuals:                      479
Model Family:                Binomial   Df Model:                            1
Link Function:                  logit   Scale:                          1.0000
Method:                          IRLS   Log-Likelihood:                -186.18
Date:                Fri, 07 Feb 2020   Deviance:                       372.35
Time:                        12:45:10   Pearson chi2:                     436.
No. Iterations:                     6                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
const        -60.7401      5.182    -11.722      0.000     -70.896     -50.584
x             34.2859      2.913     11.769      0.000      28.576      39.996
==============================================================================










    






/home/cmb-06/as/skchoudh/software_frozen/anaconda37/envs/riboraptor/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.
Use an instance of a link class instead.
  """Entry point for launching an IPython kernel.

















In [ ]:

Content source: saketkc/notebooks

Similar notebooks:

notebook.community | gallery | about