# 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 : import statsmodels.api as sm

# Logit Model
In : logit_mod = sm.Logit(spector_data.endog, spector_data.exog)

In : logit_res = logit_mod.fit()
Optimization terminated successfully.
Current function value: 0.402801
Iterations 7

In : print(logit_res.summary())
Logit Regression Results
==============================================================================
Dep. Variable:                  GRADE   No. Observations:                   32
Model:                          Logit   Df Residuals:                       28
Method:                           MLE   Df Model:                            3
Date:                Tue, 27 Oct 2020   Pseudo R-squ.:                  0.3740
Time:                        03:32:30   Log-Likelihood:                -12.890
converged:                       True   LL-Null:                       -20.592
Covariance Type:            nonrobust   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
GPA            2.8261      1.263      2.238      0.025       0.351       5.301
TUCE           0.0952      0.142      0.672      0.501      -0.182       0.373
PSI            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.

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[, check_rank]) Logit Model Probit(endog, exog[, check_rank]) Probit Model MNLogit(endog, exog[, check_rank]) Multinomial Logit Model Poisson(endog, exog[, offset, exposure, …]) Poisson Model NegativeBinomial(endog, exog[, …]) Negative Binomial Model NegativeBinomialP(endog, exog[, p, offset, …]) Generalized Negative Binomial (NB-P) Model GeneralizedPoisson(endog, exog[, p, offset, …]) Generalized Poisson Model
 ZeroInflatedPoisson(endog, exog[, …]) Poisson Zero Inflated Model ZeroInflatedNegativeBinomialP(endog, exog[, …]) Zero Inflated Generalized Negative Binomial Model ZeroInflatedGeneralizedPoisson(endog, exog) Zero Inflated Generalized Poisson Model
 ConditionalLogit(endog, exog[, missing]) Fit a conditional logistic regression model to grouped data. ConditionalMNLogit(endog, exog[, missing]) Fit a conditional multinomial logit model to grouped data. ConditionalPoisson(endog, exog[, missing]) Fit a conditional Poisson regression model to grouped data.
 OrderedModel(endog, exog[, offset, distr]) Ordinal Model based on logistic or normal distribution

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 A results class for Zero Inflated Generalized Negative Binomial A results class for Zero Inflated Generalized Poisson
 OrderedResults(model, mlefit) Attributes

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[, check_rank]) Abstract class for discrete choice models. DiscreteResults(model, mlefit[, cov_type, …]) A results class for the discrete dependent variable models. BinaryModel(endog, exog[, check_rank]) Attributes BinaryResults(model, mlefit[, cov_type, …]) A results class for binary data CountModel(endog, exog[, offset, exposure, …]) Attributes MultinomialModel(endog, exog[, check_rank]) Attributes
 GenericZeroInflated(endog, exog[, …]) Generic Zero Inflated Model