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 inmarginal parameterizations tomodel simultaneously, and conditionally on individual covariates, the size of the latent classes, themarginal 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 formaximum likelihood estimation is described, and an expression for the expected informationmatrix is derived. In addition, a new method for computing confidence intervals for the size of the population having given covariate configurations isproposed and itsasymptotic properties are derived. Applications todata on patients with human immunodeficiency virus, in the region of V?neto, Italy, and to new cases of cancer inTuscany are discussed.