Parameter identifiability and model selection in capture-recapture models: A numerical approach

Capture-recapture models are a powerful tool for estimating and comparing survival probabilities among groups of individuals in wild animal populations. One of the remaining problems is the calculation of the number of independently estimable parameters in the models, which is necessary in using model selection tools such as Likelihood ratio tests or the Akaike's information Criterion. We show that the number of separately identifiable parameters in a model is equal to the rank of the Hessian matrix (second derivatives of the maximum likelihood relative to the parameters). We present the numerical problems involved in computing the Hessian and its numerical rank, and we apply the technique to data on nesting swifts (Apus apus).