Abstract
Hidden Markov models (HMMs) are being widely used in the field of ecological modelling, however determining the number of underlying states in an HMM remains a challenge. Here we examine a special case of partially observed capture-recapture models for open populations, where some animals are observed but it is not possible to ascertain their state (partial observations), whilst the other animals' states are assigned without error (complete observations). We propose a mixture test of the underlying state structure generating the partial observations, which assesses whether they are compatible with the set of states directly observed in the complete observationscapture-recapture experiment. We demonstrate the good performance of the test using simulation and through application to a data set of Canada Geese. This paper provides a novel method to offer practical insight to a large class of HMM applications.