Discrete Choice Models Overview



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import numpy as np
import statsmodels.api as sm

Data

Load data from Spector and Mazzeo (1980). Examples follow Greene's Econometric Analysis Ch. 21 (5th Edition).



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spector_data = sm.datasets.spector.load()
spector_data.exog = sm.add_constant(spector_data.exog, prepend=False)

Inspect the data:



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print spector_data.exog[:5,:]
print spector_data.endog[:5]

Linear Probability Model (OLS)



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lpm_mod = sm.OLS(spector_data.endog, spector_data.exog)
lpm_res = lpm_mod.fit()
print 'Parameters: ', lpm_res.params[:-1]

Logit Model



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logit_mod = sm.Logit(spector_data.endog, spector_data.exog)
logit_res = logit_mod.fit(disp=0)
print 'Parameters: ', logit_res.params

Marginal Effects



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margeff = logit_res.get_margeff()
print margeff.summary()

As in all the discrete data models presented below, we can print a nice summary of results:



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print logit_res.summary()

Probit Model



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probit_mod = sm.Probit(spector_data.endog, spector_data.exog)
probit_res = probit_mod.fit()
probit_margeff = probit_res.get_margeff()
print 'Parameters: ', probit_res.params
print 'Marginal effects: '
print probit_margeff.summary()

Multinomial Logit

Load data from the American National Election Studies:



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anes_data = sm.datasets.anes96.load()
anes_exog = anes_data.exog
anes_exog = sm.add_constant(anes_exog, prepend=False)

Inspect the data:



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print anes_data.exog[:5,:]
print anes_data.endog[:5]

Fit MNL model:



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mlogit_mod = sm.MNLogit(anes_data.endog, anes_exog)
mlogit_res = mlogit_mod.fit()
print mlogit_res.params

Poisson

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.



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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:



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poisson_mod = sm.Poisson(rand_data.endog, rand_exog)
poisson_res = poisson_mod.fit(method="newton")
print poisson_res.summary()

Negative Binomial

The negative binomial model gives slightly different results.



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mod_nbin = sm.NegativeBinomial(rand_data.endog, rand_exog)
res_nbin = mod_nbin.fit(disp=False)
print res_nbin.summary()

Alternative solvers

The default method for fitting discrete data MLE models is Newton-Raphson. You can use other solvers by using the method argument:



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mlogit_res = mlogit_mod.fit(method='bfgs', maxiter=100)
print mlogit_res.summary()