Estimating the size of a closed population by modeling latent and observed heterogeneity

The paper describes a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model for capture probabilities where the class weights and the conditional distributions given the latent may depend on covariates, with a model for the marginal distribution of the available covariates as in Liu et al, Biometrika (2017). In addition, the conditional distributions given the latent and covariates are allowed to take into account any general form of serial dependence. A Fisher scoring algorithm for maximum likelihood estimation is presented, and a powerful result based on the implicit function theorem is used to show that the marginal distribution of observed covariates is uniquely determined, once an estimate of the probabilities of being never captured is available. Asymptotic results are outlined, and a procedure for constructing likelihood based confidence intervals for the population total is presented. Two examples with real data are used to illustrate the proposed approach