Testing list effects and diagnosing individual catchabilities in the Rasch model

The Rasch model is useful in the problem of estimating the population size from multiple incomplete lists. It is of great interest to tell whether there are list effects and whether individuals differ in their catchabilities. These two important model selection problems can be easily addressed conditionally. A conditional likelihood ratio test is used to evaluate the list effects and several graphical methods are used to diagnose the individual catchabilities, while neither the unknown population size nor the unknown mixing distribution of individual catchabilities is required to be estimated. Three epidemiological applications are used for illustration.