import numpy as np
import statsmodels.api as sm
Load data from Spector and Mazzeo (1980). Examples follow Greene's Econometric Analysis Ch. 21 (5th Edition).
spector_data = sm.datasets.spector.load()
spector_data.exog = sm.add_constant(spector_data.exog, prepend=False)
Inspect the data:
print spector_data.exog[:5,:]
print spector_data.endog[:5]
[[ 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.]
lpm_mod = sm.OLS(spector_data.endog, spector_data.exog)
lpm_res = lpm_mod.fit()
print 'Parameters: ', lpm_res.params[:-1]
Parameters: [ 0.46385168 0.01049512 0.37855479]
logit_mod = sm.Logit(spector_data.endog, spector_data.exog)
logit_res = logit_mod.fit()
print 'Parameters: ', logit_res.params
print 'Marginal effects: ', logit_res.margeff()
Optimization terminated successfully. Current function value: 12.889634 Iterations 7 Parameters: [ 2.82611259 0.09515766 2.37868766 -13.02134686] Marginal effects: [ 0.36258083 0.01220841 0.3051777 ]
As in all the discrete data models presented below, we can print a nice summary of results:
print logit_res.summary()
Logit Regression Results ============================================================================== Dep. Variable: y No. Observations: 32 Model: Logit Df Residuals: 28 Method: MLE Df Model: 3 Date: Sun, 26 Aug 2012 Pseudo R-squ.: 0.3740 Time: 20:48:40 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 ==============================================================================
probit_mod = sm.Probit(spector_data.endog, spector_data.exog)
probit_res = probit_mod.fit()
print 'Parameters: ', probit_res.params
print 'Marginal effects: ', probit_res.margeff()
Optimization terminated successfully. Current function value: 12.818804 Iterations 6 Parameters: [ 1.62581004 0.05172895 1.42633234 -7.45231965] Marginal effects: [ 0.36078629 0.01147926 0.31651986]
Load data from the American National Election Studies:
anes_data = sm.datasets.anes96.load()
anes_exog = anes_data.exog
anes_exog[:,0] = np.log(anes_exog[:,0] + .1)
anes_exog = np.column_stack((anes_exog[:,0],anes_exog[:,2],anes_exog[:,5:8]))
anes_exog = sm.add_constant(anes_exog, prepend=False)
Inspect the data:
print anes_data.exog[:5,:]
print anes_data.endog[:5]
[[ -2.30258509 7. 7. 1. 6. 36. 3. 1. 1. ] [ 5.24755025 1. 3. 3. 5. 20. 4. 1. 0. ] [ 3.43720782 7. 2. 2. 6. 24. 6. 1. 0. ] [ 4.4200447 4. 3. 4. 5. 28. 6. 1. 0. ] [ 6.46162441 7. 5. 6. 4. 68. 6. 1. 0. ]] [ 6. 1. 1. 1. 0.]
Fit MNL model:
mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog)
mlogit_res = mlogit_mod.fit()
print mlogit_res.params
Optimization terminated successfully. Current function value: 1461.922747 Iterations 7 [[ -0.01153597 -0.08875065 -0.1059667 -0.0915567 -0.0932846 -0.14088069] [ 0.29771435 0.39166864 0.57345051 1.27877179 1.34696165 2.07008014] [ -0.024945 -0.02289784 -0.01485121 -0.00868135 -0.01790407 -0.00943265] [ 0.08249144 0.18104276 -0.00715242 0.19982796 0.21693885 0.3219257 ] [ 0.00519655 0.04787398 0.05757516 0.08449838 0.08095841 0.10889408] [ -0.37340168 -2.25091318 -3.66558353 -7.61384309 -7.06047825 -12.1057509 ]]
Load the Rand data. Note that this example is similar to Cameron and Trivedi's Microeconometrics
Table 20.5, but it is slightly different because of minor changes in the data.
rand_data = sm.datasets.randhie.load()
rand_exog = rand_data.exog.view(float).reshape(len(rand_data.exog), -1)
rand_exog = sm.add_constant(rand_exog, prepend=False)
Fit Poisson model:
poisson_mod = sm.Poisson(rand_data.endog, rand_exog)
poisson_res = poisson_mod.fit(method="newton")
print poisson_res.summary()
Optimization terminated successfully. Current function value: 62419.588564 Iterations 12 Poisson Regression Results ============================================================================== Dep. Variable: y No. Observations: 20190 Model: Poisson Df Residuals: 20180 Method: MLE Df Model: 9 Date: Sun, 26 Aug 2012 Pseudo R-squ.: 0.06343 Time: 20:48:46 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 ==============================================================================
The default method for fitting discrete data MLE models is Newton-Raphson. You can use other solvers by using the method
argument:
mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=100)
print mlogit_res.summary()
Optimization terminated successfully. Current function value: 1461.922747 Iterations: 54 Function evaluations: 98 Gradient evaluations: 89 MNLogit Regression Results ============================================================================== Dep. Variable: y No. Observations: 944 Model: MNLogit Df Residuals: 908 Method: MLE Df Model: 30 Date: Sun, 26 Aug 2012 Pseudo R-squ.: 0.1648 Time: 20:48:54 Log-Likelihood: -1461.9 converged: True LL-Null: -1750.3 LLR p-value: 1.822e-102 ============================================================================== y=1 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0115 0.034 -0.336 0.736 -0.079 0.056 x2 0.2977 0.094 3.180 0.001 0.114 0.481 x3 -0.0249 0.007 -3.823 0.000 -0.038 -0.012 x4 0.0825 0.074 1.121 0.262 -0.062 0.227 x5 0.0052 0.018 0.295 0.768 -0.029 0.040 const -0.3734 0.630 -0.593 0.553 -1.608 0.861 ------------------------------------------------------------------------------ y=2 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0888 0.039 -2.266 0.023 -0.166 -0.012 x2 0.3917 0.108 3.619 0.000 0.180 0.604 x3 -0.0229 0.008 -2.893 0.004 -0.038 -0.007 x4 0.1810 0.085 2.123 0.034 0.014 0.348 x5 0.0479 0.022 2.149 0.032 0.004 0.092 const -2.2509 0.763 -2.949 0.003 -3.747 -0.755 ------------------------------------------------------------------------------ y=3 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.1060 0.057 -1.858 0.063 -0.218 0.006 x2 0.5735 0.159 3.617 0.000 0.263 0.884 x3 -0.0149 0.011 -1.311 0.190 -0.037 0.007 x4 -0.0072 0.126 -0.057 0.955 -0.255 0.240 x5 0.0576 0.034 1.713 0.087 -0.008 0.123 const -3.6656 1.157 -3.169 0.002 -5.932 -1.399 ------------------------------------------------------------------------------ y=4 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0916 0.044 -2.091 0.037 -0.177 -0.006 x2 1.2788 0.129 9.921 0.000 1.026 1.531 x3 -0.0087 0.008 -1.031 0.302 -0.025 0.008 x4 0.1998 0.094 2.123 0.034 0.015 0.384 x5 0.0845 0.026 3.226 0.001 0.033 0.136 const -7.6138 0.958 -7.951 0.000 -9.491 -5.737 ------------------------------------------------------------------------------ y=5 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.0933 0.039 -2.371 0.018 -0.170 -0.016 x2 1.3470 0.117 11.494 0.000 1.117 1.577 x3 -0.0179 0.008 -2.352 0.019 -0.033 -0.003 x4 0.2169 0.085 2.552 0.011 0.050 0.384 x5 0.0810 0.023 3.524 0.000 0.036 0.126 const -7.0605 0.844 -8.362 0.000 -8.715 -5.406 ------------------------------------------------------------------------------ y=6 coef std err z P>|z| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 -0.1409 0.042 -3.343 0.001 -0.223 -0.058 x2 2.0701 0.143 14.435 0.000 1.789 2.351 x3 -0.0094 0.008 -1.160 0.246 -0.025 0.007 x4 0.3219 0.091 3.534 0.000 0.143 0.500 x5 0.1089 0.025 4.304 0.000 0.059 0.158 const -12.1058 1.060 -11.421 0.000 -14.183 -10.028 ==============================================================================