ABSTRACT
This chapter focuses on a class of models for the analysis of capture-recapture data that can be applied when the full response configuration for each unit captured at least once is available. The model, very popular since the sixties in psychology and education, was introduced by Rasch to analyse data collected by questionnaires made of dichotomously scored items, with the objective to measure both the individual latent trait or ability and the relative difficulty of different items. The chapter provides an illustration of likelihood inference for the models and the population size on the basis of the Expectation-Maximisation (EM) algorithm. It describes a specific method for constructing a confidence interval for the population size. The chapter describes the approach of main interest, which provides an accessible illustration of the models. It describes the likelihood inference for such models. The chapter ends with two applications, which illustrates model selection and inference on the population size in two different contexts.
