Models for Underreporting: A Bernoulli Sampling Approach for Reported Counts

Underreporting in register systems can be analyzed using a binomial approach, where both the size and the probability parameter have to be estimated. Parameter estimation fails when overdispersion is present. Extensions of the binomial model are derived by randomizing the parameters, i.e. considering mixed models. Among these models are the beta-binomial, which results from allowing for a random reporting probability; the negativebinomial, that is the marginal when the size parameter is randomized; and the beta-Poisson model, where both binomial parameters are considered random. Likelihood based estimation is developed and inference issues are discussed. Finally the method is applied to data from the Austrian crime register.