Bias, precision, and parameter redundancy in complex multistate models with unobservable states

Multistate mark-recapture models with unobservable states can yield unbiased estimators of survival probabilities in the presence of temporary emigration (i.e., in cases where some individuals are temporarily unavailable for capture). In addition, these models permit the estimation of transition probabilities between states, which may themselves be of interest; for example, when only breeding animals are available for capture. However, parameter redundancy is frequently a problem in these models, yielding biased parameter estimates and influencing model selection. Using numerical methods, we examine complex multistate mark-recapture models involving two observable and two unobservable states. This model structure was motivated by two different biological systems: one involving island-nesting albatross, and another involving pond-breeding amphibians. We found that, while many models are theoretically identifiable given appropriate constraints, obtaining accurate and precise parameter estimates in practice can be difficult. Practitioners should consider ways to increase detection probabilities or adopt robust design sampling in order to improve the properties of estimates obtained from these models. We suggest that investigators interested in using these models explore both theoretical identifiability and possible near-singularity for likely parameter values using a combination of available methods.