On the identifiability of the trinomial model for mark-recapture-recovery studies

Continuous predictors of survival present a challenge in the analysis of data from studies of marked individuals if they vary over time and can only be observed when individuals are captured. Existing methods to study the effects of such variables have followed one of two approaches. The first is to model the joint distribution of the predictor and the observed capture histories, and the second is to draw inference from the likelihood conditional on events that depend only on observed predictor values, called the trinomial model. Previous comparison of these approaches found that joint modelling provided more precise inference about the effect of the covariate while the trinomial model was less prone to issues of model mis-specification. However, we believe that an important issue was missed. We show through mathematical analysis and numerical simulation that the trinomial model is not identifiable when the predictor has no effect on the survival probability. This also causes inferences from the trinomial model to be imprecise when the effect of the covariate on the survival probability is small. We also analyse data on the effect of body mass on the survival of meadow voles to demonstrate the importance of this issue in real applications.