ABSTRACT
Making inference on the size of a population of interest requires assumptions on whether the population is closed/open. This chapter presents a range of models for which identifiability has been well understood. It introduces the concepts and notations, which recall the notion of graphical models for categorical data. The chapter describes the use of log $ {\text{log }} $ -linear models in capture-recapture problems with observed categorical covariates. It presents the class of models proposed, that can be seen as an extension of Latent Class models. The chapter reviews the notion of identification while it proposes a method, based on the profile log $ {\text{log }} $ -likelihood, to construct confidence intervals for the undercounts in each stratum formed by the covariates. The proposed methods are applied to real data, in particular it analyses the underreporting of infants born with congenital anomaly in Massachusetts while it helps in studying the problem of undercount in bacterial meningitis in the Lazio region.
