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Efficient profile-likelihood confidence intervals for capture-recapture models

In a capture-recapture analysis, uncertainty in the parameter estimates is usually expressed by presenting classical Wald-type confidence intervals. This approach involves (1) the assumption that the maximum likelihood estimates are asymptotically normal and (2) numerical computation of the variance-covariance matrix of these estimates. When the sample size is small or when the estimates are on the boundary of their domain, a Wald confidence interval often performs badly. A natural alternative is to use profile-likelihood confidence intervals. In general, these intervals require a greater amount of computation. We propose a new implementation of this approach that is efficient, both in reducing the amount of computation and in coping with boundary estimates. We also show how profile-likelihood confidence intervals can be adjusted for overdispersion. Simulations were used to check whether nominal coverage levels were attained, and allowed us to compare this approach with the classical Wald procedure. We illustrate this work by considering a multi-state model for a sooty shearwater (Puffinus griseus) population.