Generalized Linear Models
Generalized linear models currently supports estimation using the one-parameter exponential families
See Module Reference for commands and arguments.
Examples
# Load modules and data import statsmodels.api 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.families.Gamma()) gamma_results = gamma_model.fit()
Detailed examples can be found here:
Technical Documentation
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.
Module Reference
Model Class
GLM (endog, exog[, family, offset, exposure, ...]) | Generalized Linear Models class |
Results Class
GLMResults (model, params, ...[, cov_type, ...]) | 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
>>> sm.families.family.<familyname>.links
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_power () | The inverse transform |
inverse_squared () | The inverse squared transform |
log | The log transform |
logit | |
nbinom ([alpha]) | The negative binomial link function. |
probit ([dbn]) | The probit (standard normal CDF) transform |
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