Laplace Approximations for Capture–Recapture Models in the Presence of Individual Heterogeneity

Capture–recapture studies are common for collecting data on wildlife populations. Populations in such studies are often subject to different forms of heterogeneity that may influence their associated demographic rates. We focus on the most challenging of these relating to individual heterogeneity. We consider (i) continuous time-varying individual covariates and (ii) individual random effects. In general, the associated likelihood is not available in closed form but only expressible as an analytically intractable integral. The integration is specified over (i) the unknown individual covariate values (if an individual is not observed, its associated covariate value is also unknown) and (ii) the unobserved random effect terms. Previous approaches to dealing with these issues include numerical integration and Bayesian data augmentation techniques. However, as the number of individuals observed and/or capture occasions increases, these methods can become computationally expensive. We propose a new and efficient approach that approximates the analytically intractable integral in the likelihood via a Laplace approximation. We find that for the situations considered, the Laplace approximation performs as well as, or better, than alternative approaches, yet is substantially more efficient.Supplementary materials accompanying this paper appear on-line