Analysis of capture-recapture data with a Rasch-type model allowing for conditional dependence and multidimensionality

In this article, we show that, if subjects are assumed to be homogeneous within it finite set of latent classes, the basic restrictions of the Rasch model (conditional independence and unidimensionality) can be relaxed in a flexible way by simply adding appropriate columns to a basic design matrix. When discrete covariates are available so that subjects may be classified into strata, we show how a joint modeling approach can achieve greater parsimony. Parameter estimates may be obtained by maximizing the conditional likelihood (given the total number of captures) with a combined use of the EM and Fisher scoring algorithms. We also discuss a technique for obtaining confidence intervals for the size of the population under study based on the profile likelihood.