Log-linear multidimensional Rasch model for capture-recapture

The traditional capture-recapture method assumes homogeneity of the capture probabilities. However, differences of character or behaviour between individuals may occur and models that allow for varying susceptibility to capture over individuals and unequal catchability have been proposed and psychometric models, such as the Rasch model, were successfully applied. In the present work, we propose the use of the multidimensional Rasch model in the capture-recapture context. We assume that lists may be divided into two or more subgroups, such that they can be viewed as indicators of the latent variables which account for correlations among lists. We show how to express the probability of a generic capture profile in terms of log-linear multidimensional Rasch model and apply the methodology to a real data set.