Analysing Mark-Recapture-Recovery Data in the Presence of Covariate Data using Multiple Imputation

Worthington, H., King, R. and Buckland, S.T.

University of St. Andrews


We consider mark-recapture-recovery data where there is additional individual time-varying continuous covariate data. For such data it is common to specify the model parameters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity within the model. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, leading to a likelihood that is only expressible as an analytically intractable integral. Within this paper we propose a two-tep multiple imputation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Secondly, conditional on the fitted covariate model, multiple ''complete'' datasets are generated (i.e. all the missing covariate values are imputed). For each complete dataset, a closed form complete-data-likelihood can be explicitly calculated and maximised to obtain estimates of the model parameters which are subsequently combined to obtain an overall estimate of the model parameters. Associated standard error and/or 95% confidence intervals are obtained using a non-parametric bootstrap, to account for additional uncertainty with regard to the underlying covariate model. A simulation study is undertaken to assessthe performance of the approach. We apply the method to data collected on a well-studied population of Soay sheep.

Keywords: Individual time-varying continuous covariates;mark-recapture-recovery data; missing values; multiple imputation; two-step algorithm.