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I want to compare model $A$ with 5 variables and model $B$ with 3 variables. I want to use the likelihood ratio test to do this. Note that this is logistic regression. How do I do this in SAS?

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    $\begingroup$ Is the three variable model a sub-model of the five variable model? If so, you can take the $-2\cdot{\rm loglike}$ from the outputs and do it manually, if nothing else. $\endgroup$ – Macro Nov 16 '11 at 1:23
  • $\begingroup$ @Macro: And you use the intercept and covariates values of $-2 \log L$ for each model and divide by 2? $\endgroup$ – Terry Nov 16 '11 at 1:38
  • $\begingroup$ No. Under the null, the difference between the $-2 \log L$ values follows a $\chi^{2}_{d}$ distribution (as $n \rightarrow \infty$) where $d$ is the number of parameters deleted to arrive at the submodel. You can use the CDF of that distribution to get the $p$-value. $\endgroup$ – Macro Nov 16 '11 at 22:59
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See this example from the documentation which shows how to construct and compare different ROC curves for the models: http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_logistic_sect066.htm

Notice in the output that each model includes the -2 log L. Also notice that the final table of this output includes the chi-square values and p-values for the pairwise comparisons.

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