Conditional and unconditional categorical regression models with missing covariates

We consider methods for analyzing categorical regression models when some covariates (Z) are completely observed but other covariates (X) are missing for some subjects. When data on X are missing at random (i.e., when the probability that X is observed does not depend on the value of X itself), we present a likelihood approach for the observed data that allows the same nuisance parameters to be eliminated in a conditional analysis as when data are complete. An example of a matched case-control study is used to demonstrate our approach.