Fitting Logistic Models Under Case-Control or Choice Based Sampling

SUMMARY There has been a great deal of interest in recent years in fitting logistic and log-linear models to tables of population counts estimated from survey data. Since maximum likelihood methods are not available in general for complex survey designs, most work has concentrated on adapting standard methods developed for multinomial sampling. Maximum likelihood methods have been developed for some special designs, however, and we might expect ad hoc methods to be less efficient in these cases. We compare the two approaches in the important special case of fitting logistic regression models under case-control or choice-based sampling, where the population is stratified by values of the (categorical) response variable.