A class of latent marginal models for capture-recapture data with continuous covariates

We introduce a new family of latent class models for the analysis of capture-recapture data where continuous covariates are available. The present approach exploits recent advances in marginal parameterizations to model simultaneously, and conditionally on individual covariates, the size of the latent classes, the marginal probabilities of being captured by each list given the latent, and possible higher-order marginal interactions among lists conditionally on the latent. An EM algorithm for maximum likelihood estimation is described, and an expression for the expected information matrix is derived. In addition, a new method for computing confidence intervals for the size of the population having given covariate configurations is proposed and its asymptotic properties are derived. Applications to data on patients with human immunodeficiency virus, in the region of Veneto, Italy, and to new cases of cancer in Tuscany are discussed.