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

TL;DR

This paper introduces a novel capture-recapture model for closed populations that incorporates individual covariates and latent heterogeneity, allowing for flexible dependence structures and providing maximum likelihood estimation methods.

Contribution

It combines latent class modeling with covariate-dependent class weights and distributions, offering a new approach to estimate population size with heterogeneity.

Findings

Effective maximum likelihood estimation via Fisher-scoring

One-to-one mapping between covariate distribution and capture probabilities

Successful application to real data examples

Abstract

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 the distribution of the capture history, 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 \cite{Liu2017}. In addition, any general form of serial dependence is allowed when modeling capture histories conditionally on the latent and covariates. A Fisher-scoring algorithm for maximum likelihood estimation is proposed, and the Implicit Function Theorem is used to show that the mapping between the marginal distribution of the observed covariates and the probabilities of being never captured is one-to-one. Asymptotic results are outlined, and a procedure for constructing likelihood based confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach