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# Generalized Linear Models

## Introduction

Generalized linear models currently supports estimation using the one-parameter exponential families

### References

Gill, Jeff. 2000. Generalized Linear Models: A Unified Approach.
  SAGE QASS Series.
Green, PJ. 1984. “Iteratively reweighted least squares for maximum
  likelihood estimation, and some robust and resistant alternatives.” Journal of the Royal Statistical Society, Series B, 46, 149-192.
Hardin, J.W. and Hilbe, J.M. 2007. “Generalized Linear Models and
  Extensions.” 2nd ed. Stata Press, College Station, TX.
McCullagh, P. and Nelder, J.A. 1989. “Generalized Linear Models.” 2nd ed.
  Chapman & Hall, Boca Rotan.

## Examples

>     >>> import scikits.statsmodels as sm
>     >>> data = sm.datasets.scotland.Load()
>     >>> data.exog = sm.add_constant(data.exog)

> Instantiate a gamma family model with the default link function.

>     >>> gamma_model = sm.GLM(data.endog, data.exog,
>             family=sm.family.Gamma())
>     >>> gamma_results = gamma_model.fit()

see also the examples and the tests folders

## Module Reference

### Model and Result Classes

`GLM`(endog, exog[, family]) | Generalized Linear Models class
`GLMResults`(model, params, ...) | Class to contain GLM results.

### Families

The distribution families currently implemented are

`Family`(link, variance) | The parent class for one-parameter exponential families.
`Binomial`([link]) | Binomial exponential family distribution.
`Gamma`([link]) | Gamma exponential family distribution.
`Gaussian`([link]) | Gaussian exponential family distribution.
`InverseGaussian`([link]) | InverseGaussian exponential family.
`NegativeBinomial`([link, alpha]) | Negative Binomial exponential family.
`Poisson`([link]) | Poisson exponential family.

### Link Functions

The link functions currently implemented are the following. Not all link functions are available for each distribution family. The list of available link functions can be obtained by

    >>> ssm.family.family.<familyname>.available ?

`Link` | A generic link function for one-parameter exponential family.
`CDFLink`([dbn]) | The use the CDF of a scipy.stats distribution
`CLogLog` | The complementary log-log transform
`Log` | The log transform ..
`Logit` | The logit transform ..
`NegativeBinomial`([alpha]) | The negative binomial link function
`Power`([power]) | The power transform
`cauchy` | The Cauchy (standard Cauchy CDF) transform
`cloglog` | The CLogLog transform link function.
`identity` | The identity transform ..
`inverse` | The inverse transform ..
`inverse_squared` | The inverse squared transform ..
`log` | The log transform ..
`logit` | The logit transform ..
`nbinom` | The negative binomial link function.
`probit` | The probit (standard normal CDF) transform

## Technical Documentation

- Technical Documentation
- Technical Documentation - part 2

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