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# Regression with Discrete Dependent Variable

Note: These models have just been moved out of the sandbox. Large parts of the statistical results are verified and tested, but this module has not seen much use yet and we can still expect some changes.

## Introduction

:mod:discretemod contains regression models for limited dependent and qualitative variables.

This currently includes models when the dependent variable is discrete, either binary (Logit, Probit), (ordered) ordinal data (MNLogit) or count data (Poisson). 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.

Example:

    # Load the data from Spector and Mazzeo (1980)
    spector_data = sm.datasets.spector.Load()
    spector_data.exog = sm.add_constant(spector_data.exog)

    # Linear Probability Model using OLS
    lpm_mod = sm.OLS(spector_data.endog,spector_data.exog)
    lpm_res = lpm_mod.fit()

    # Logit Model
    logit_mod = sm.Logit(spector_data.endog, spector_data.exog)
    logit_res = logit_mod.fit()

    # Probit Model
    probit_mod = sm.Probit(spector_data.endog, spector_data.exog)
    probit_res = probit_mod.fit()

    # Since the parameters have different parameterization across non-linear
    # models, we can use the average marginal effect instead to compare the
    # models results.

    >>> lpm_res.params[:-1]
    array([ 0.46385168,  0.01049512,  0.37855479])
    >>> logit_res.margeff()
    array([ 0.36258083,  0.01220841,  0.3051777 ])
    >>> probit_res.margeff()
    array([ 0.36078629,  0.01147926,  0.31651986])

### 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.

23. Greene. Econometric Analysis. Prentice Hall, 5th. edition. 2003.

### Examples

see the examples and the tests folders, and the docstrings of the individual model classes.

## Module Reference

The specific model classes are:

`Logit`(endog[, exog]) | Binary choice logit model
`Probit`(endog[, exog]) | Binary choice Probit model
`MNLogit`(endog[, exog]) | Multinomial logit model
`Poisson`(endog[, exog]) | Poisson model for count data

`DiscreteModel` is a superclass of all discrete regression models. The estimation results are returned as an instance of `DiscreteResults`

`DiscreteModel`(endog[, exog]) | Abstract class for discrete choice models.
`DiscreteResults`(model, params, hessian[, scale]) | A results class for the discrete dependent variable models.

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