The utility of mixed-form likelihoods

We highlight a feature of likelihood-based methods that provides flexibility in model formulation and inference. In particular, overall likelihoods that consist of likelihood contributions with different forms are considered. The particular forms may be predetermined by design criteria or may be selected based on features of the data. Inferences based on such mixed-form likelihoods are valid provided standard regularity conditions hold and the parameters of interest have the same interpretation in the various forms. The advantages of constructing overall likelihoods in this way are illustrated by applications involving the analysis of 2 x 2 x K tables and left-censored water quality data.