A multidimensional Rasch model for multiple system estimation where the number of lists changes over time

This chapter discusses the estimation of the population size in a capture-recapture context using the log-linear multidimensional Rasch model. This model can be used in those situations with two or more incomplete and overlapping lists of cases available from different sources. Under the assumption that lists can be viewed as indicators of the latent variables which account for correlations among lists it is shown how the probability of a generic capture profile can be easily expressed in a log-linear form. The model is discussed either in the case with or without a stratifying variable is available. The chapter also shows how the proposed model can be performed when lists refer to different populations (e.g. different periods of time or regions). In such cases, lists that are not observed are assumed to be missing and the EM algorithm is used to estimate the missing values. Finally, an application to real data set on children born with a neural tube defect in the Netherlands during the years 1988 through 1998 is presented and results on the yearly estimates of the incidence of spina bifida are discussed.