7.2. Generalized Linear Models¶
Generalized linear models currently supports estimation using the one-parameter exponential families
See Module Reference for commands and arguments.
7.2.1. 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:
7.2.2. Technical Documentation¶
7.2.2.1. 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.
7.2.3. Module Reference¶
7.2.3.1. Model Class¶
GLM (endog, exog[, family, offset, exposure, ...]) |
Generalized Linear Models class |
7.2.3.2. Results Class¶
GLMResults (model, params, ...[, cov_type, ...]) |
Class to contain GLM results. |
7.2.3.3. 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. |
7.2.3.4. 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 |