A likelihood ratio test that compares two nested models can be computed when the models are fit by maximum likelihood. Two models are nested when one model is a special case of the other so that one model is considered the full model and the other is a reduced model. Given the full log likelihood values for the full and reduced models, the likelihood ratio test statistic is easily computed as -2 times the positive difference in the log likelihood values. See this note which uses a simple DATA step to compute the likelihood ratio test and its p-value to compare full and reduced models fit in PROC PHREG. The same code can be used to conduct the test for models fit by other maximum likelihood procedures.

For models fit in PROC GENMOD, the likelihood ratio test can also be done with the CONTRAST statement. See Example 4 in Examples of Writing CONTRAST and ESTIMATE Statements for a discussion and illustration. More generally, this can be done by fitting the full and reduced models and saving their predicted values. The test can then be performed by the Vuong macro. See Example 8 in Vuong macro documentation for an example.

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