A capture-recapture method that takes observed and unobserved heterogeneity into account

In epidemiology the capture-recapture methodology is often used to estimate the size of an unknown population from a number of lists. One of the assumptions underlying this methodology is the homogeneity of capture probabilities of individuals. This assumption is often violated, and when it has been violated this leads to interactions between lists. Two approaches exist for taking possible heterogeneity into account. The first is to incorporate observed heterogeneity into the model by letting, for example, capture probabilities be a function covariates. A more recent approach concentrates on unobserved heterogeneity alone, and models this by using latent variables. An example is the latent class model. We extend the model by letting the parameters of the latent class model be functions of covariates. Unobserved heterogeneity is taken into account by the usage of the latent class model. Observed heterogeneity is taken into account in two ways. First, in each class of the latent class model the probabilities to fall in each of the lists are not homogeneous anymore because they differ over individuals as a function of their covariates. Second, membership of latent classes is also not homogeneous anymore but a function of covariates. We illustrate the usefulness of this model with an example where we estimate the prevalence of diabetes in Italy.