Regression with Discrete Dependent Variable¶
Regression models for limited and qualitative dependent variables. The module currently allows the estimation of models with binary (Logit, Probit), nominal (MNLogit), or count (Poisson, NegativeBinomial) data.
Starting with version 0.9, this also includes new count models, that are still experimental in 0.9, NegativeBinomialP, GeneralizedPoisson and zero-inflated models, ZeroInflatedPoisson, ZeroInflatedNegativeBinomialP and ZeroInflatedGeneralizedPoisson.
See Module Reference for commands and arguments.
Examples¶
# Load the data from Spector and Mazzeo (1980)
In [1]: spector_data = sm.datasets.spector.load()
In [2]: spector_data.exog = sm.add_constant(spector_data.exog)
# Logit Model
In [3]: logit_mod = sm.Logit(spector_data.endog, spector_data.exog)
In [4]: logit_res = logit_mod.fit()
Optimization terminated successfully.
Current function value: 0.402801
Iterations 7
In [5]: print(logit_res.summary())
Logit Regression Results
==============================================================================
Dep. Variable: y No. Observations: 32
Model: Logit Df Residuals: 28
Method: MLE Df Model: 3
Date: Mon, 14 May 2018 Pseudo R-squ.: 0.3740
Time: 21:46:24 Log-Likelihood: -12.890
converged: True LL-Null: -20.592
LLR p-value: 0.001502
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const -13.0213 4.931 -2.641 0.008 -22.687 -3.356
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
==============================================================================
Detailed examples can be found here:
Technical Documentation¶
Currently all models are estimated by Maximum Likelihood and assume independently and identically distributed errors.
All discrete regression models define the same methods and follow the same structure, which is similar to the regression results but with some methods specific to discrete models. Additionally some of them contain additional model specific methods and attributes.
References¶
General references for this class of models are:
A.C. Cameron and P.K. Trivedi. `Regression Analysis of Count Data`.
Cambridge, 1998
G.S. Madalla. `Limited-Dependent and Qualitative Variables in Econometrics`.
Cambridge, 1983.
W. Greene. `Econometric Analysis`. Prentice Hall, 5th. edition. 2003.
Module Reference¶
The specific model classes are:
Logit(endog, exog, **kwargs) |
Binary choice logit model |
Probit(endog, exog, **kwargs) |
Binary choice Probit model |
MNLogit(endog, exog, **kwargs) |
Multinomial logit model |
Poisson(endog, exog[, offset, exposure, missing]) |
Poisson model for count data |
NegativeBinomial(endog, exog[, …]) |
Negative Binomial Model for count data |
NegativeBinomialP(endog, exog[, p, offset, …]) |
Generalized Negative Binomial (NB-P) model for count data |
GeneralizedPoisson(endog, exog[, p, offset, …]) |
Generalized Poisson model for count data |
ZeroInflatedPoisson(endog, exog[, …]) |
Poisson Zero Inflated model for count data |
ZeroInflatedNegativeBinomialP(endog, exog[, …]) |
Zero Inflated Generalized Negative Binomial model for count data |
ZeroInflatedGeneralizedPoisson(endog, exog) |
Zero Inflated Generalized Poisson model for count data |
The specific result classes are:
LogitResults(model, mlefit[, cov_type, …]) |
A results class for Logit Model |
ProbitResults(model, mlefit[, cov_type, …]) |
A results class for Probit Model |
CountResults(model, mlefit[, cov_type, …]) |
A results class for count data |
MultinomialResults(model, mlefit[, …]) |
A results class for multinomial data |
NegativeBinomialResults(model, mlefit[, …]) |
A results class for NegativeBinomial 1 and 2 |
GeneralizedPoissonResults(model, mlefit[, …]) |
A results class for Generalized Poisson |
ZeroInflatedPoissonResults(model, mlefit[, …]) |
A results class for Zero Inflated Poisson |
ZeroInflatedNegativeBinomialResults(model, …) |
A results class for Zero Inflated Genaralized Negative Binomial |
ZeroInflatedGeneralizedPoissonResults(model, …) |
A results class for Zero Inflated Generalized Poisson |
DiscreteModel is a superclass of all discrete regression models. The
estimation results are returned as an instance of one of the subclasses of
DiscreteResults. Each category of models, binary, count and
multinomial, have their own intermediate level of model and results classes.
This intermediate classes are mostly to facilitate the implementation of the
methods and attributes defined by DiscreteModel and
DiscreteResults.
DiscreteModel(endog, exog, **kwargs) |
Abstract class for discrete choice models. |
DiscreteResults(model, mlefit[, cov_type, …]) |
A results class for the discrete dependent variable models. |
BinaryModel(endog, exog, **kwargs) |
|
BinaryResults(model, mlefit[, cov_type, …]) |
A results class for binary data |
CountModel(endog, exog[, offset, exposure, …]) |
|
MultinomialModel(endog, exog, **kwargs) |
GenericZeroInflated(endog, exog[, …]) |
Generiz Zero Inflated model for count data |