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pythonstatisticsmodelsstatsmodels

Likelihood ratio test statsmodels

In statsmodels ordinary least squares have likelihood ratio test implemented

OLSResults.compare_lr_test(restricted)

That is not true for the generalized linear model (GLM). I tried to implemtent copyng the OLS implementation:

from scipy import stats

llf_full = results.llf
llf_restr = results_res.llf
df_full = results.df_resid 
df_restr = results_res.df_resid 
lrdf = (df_restr - df_full)
lrstat = -2*(llf_restr - llf_full)
lr_pvalue = stats.chi2.sf(lrstat, df=lrdf)
lr_pvalue

it looks strightforward, but the fact that this is not implemented make me suspicious. Is this correct?

Solution

  • I don't see any problem.

    Generalized Linear Models are Maximum Likelihood models, if the scale is the one implied by the family.

    statsmodels.GLM doesn't currently implement Quasi-Likelihood methods where the scale can deviate from those of the underlying family, e.g. overdispersed Poisson, so the Likelihood Ratio test can be applied.

    implementation detail: compare_lr_test was supposed to be added for all LikelihoodModels, but I didn't check whether it's correct (or raises exception) for all models that inherit from it.