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(as_pandas=False)
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(as_pandas=False)
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(as_pandas=False)
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())