On the near-singularity of models for animal recovery data

Certain probability models sometimes provide poor descriptions when fitted to data by maximum likelihood. We examine one such model for the survival o f wild animals, which is fitted to two sets of data. When the model behaves poorly, its expected information matrix, evaluated at the maximum likeliho od estimate of parameters, has a 'small' smallest eigenvalue. This is due t o the fitted model being similar to a parameter-redundant submodel. In this case, model parameters that are precisely estimated have small coefficient s in the eigenvector corresponding to the smallest eigenvalue. Approximate algebraic expressions are provided for the smallest eigenvalue. We discuss the general applicability of these results.