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 Class

GLM(endog, exog[, family])

Generalized Linear Models class

Results Class

GLMResults(model, params, ...)

Class to contain GLM results.

Families

The distribution families currently implemented are

Family
Binomial
Gamma
Gaussian
InverseGaussian
NegativeBinomial
Poisson

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
CDFLink
CLogLog
Log
Logit
NegativeBinomial
Power
cauchy
cloglog
identity
inverse
inverse_squared
log
logit
nbinom
probit

Technical Documentation

• Technical Documentation
• Technical Documentation - part 2