Generalized linear models currently supports estimation using the one-parameter exponential families
See Module Reference for commands and arguments.
# Load modules and data
In [1]: import statsmodels.api as sm
In [2]: data = sm.datasets.scotland.load()
In [3]: data.exog = sm.add_constant(data.exog)
# Instantiate a gamma family model with the default link function.
In [4]: gamma_model = sm.GLM(data.endog, data.exog, family=sm.families.Gamma())
In [5]: gamma_results = gamma_model.fit()
In [6]: print(gamma_results.summary())
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: y No. Observations: 32
Model: GLM Df Residuals: 24
Model Family: Gamma Df Model: 7
Link Function: inverse_power Scale: 0.00358428317349
Method: IRLS Log-Likelihood: -83.017
Date: Tue, 20 Sep 2016 Deviance: 0.087389
Time: 03:37:04 Pearson chi2: 0.0860
No. Iterations: 4
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0178 0.011 -1.548 0.122 -0.040 0.005
x1 4.962e-05 1.62e-05 3.060 0.002 1.78e-05 8.14e-05
x2 0.0020 0.001 3.824 0.000 0.001 0.003
x3 -7.181e-05 2.71e-05 -2.648 0.008 -0.000 -1.87e-05
x4 0.0001 4.06e-05 2.757 0.006 3.23e-05 0.000
x5 -1.468e-07 1.24e-07 -1.187 0.235 -3.89e-07 9.56e-08
x6 -0.0005 0.000 -2.159 0.031 -0.001 -4.78e-05
x7 -2.427e-06 7.46e-07 -3.253 0.001 -3.89e-06 -9.65e-07
==============================================================================
Detailed examples can be found here:
GLMResults(model, params, ...[, cov_type, ...]) | Class to contain GLM results. |
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. |
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 | Methods |
nbinom([alpha]) | The negative binomial link function. |
probit([dbn]) | The probit (standard normal CDF) transform |