Maximum likelihood estimation of mark-recapture-recovery models in the presence of continuous covariates

TL;DR

This paper develops a maximum likelihood estimation method for mark-recapture-recovery models with continuous, time-varying covariates by discretizing the covariate space and using a hidden Markov model framework, improving analysis of animal survival data.

Contribution

It introduces a novel approximate likelihood approach for MRR models with continuous covariates, enabling efficient maximum likelihood estimation using a state-space and hidden Markov model framework.

Findings

The method effectively estimates survival probabilities with continuous covariates.

Application to Soay sheep data shows the AR(1) model fits better than diffusive models.

Simulation studies validate the approach's accuracy and efficiency.

Abstract

We consider mark-recapture-recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a state-space framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of diffusive random walks. We consider an alternative nondiffusive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.