Log-linear multidimensional Rasch model for capture-recapture

One of the most important task for epidemiologists, biologists, ecologists and sociologists is to analyse and forecast possible changes and dynamics in a population. Capture-recapture experiments may be used to obtain meaningful information from population under study. The rational behind this method is to account for unobserved individuals by using observed individual trapping histories. A central assumption in traditional capture-recapture approach is the homogeneity of the capture probability. However, differences of character or behaviour between individuals may occur and this fact results in indirect dependence between registrations. Psychometric models, such as the Rasch model, may be successfully applied. We propose the use of the multidimensional Rasch model in the capture-recapture context. In particular, we assume that registrations may be divided into two or more subgroups, such that they can be view as indicators of the latent variables which account for correlations among registrations. To do so, the extension of the Dutch Identity for the multidimensional partial credit model can be utilized. It allows us to express the multidimensional Rasch model in a log-linear representation and to derive the parameters of the traditional log-linear model from those of the multidimensional Rasch model.