Supplementary materials for this article are available at 10.1007/s13253-014-0184-z. Analysing Mark–Recapture–Recovery Data in the Presence of Missing Covariate Data

We consider mark–recapture–recovery data with additional individual time-varying continuous covariate data. For such data it is common to specify the model parame-ters, and in particular the survival probabilities, as a function of these covariates to incorporate individual heterogeneity. However, an issue arises in relation to missing covariate values, for (at least) the times when an individual is not observed, lead-ing to an analytically intractable likelihood. We propose a two-step multiple impu-tation approach to obtain estimates of the demographic parameters. Firstly, a model is fitted to only the observed covariate values. Conditional on the fitted covariate model, multiple “complete ” datasets are generated (i.e. all missing covariate values are imputed). Secondly, for each complete dataset, a closed form complete data like-lihood can be maximised to obtain estimates of the model parameters which are sub-sequently combined to obtain an overall estimate of the parameters. Associated stan-dard errors and 95 % confidence intervals are obtained using a non-parametric boot-strap. A simulation study is undertaken to assess the performance of the proposed two-step approach. We apply the method to data collected on a well-studied population of Soay sheep and compare the results with a Bayesian data augmentation approach. Supplementary materials accompanying this paper appear on-line. Key Words: Individual time-varying continuous covariates; Mark–recapture–recovery data; Missing values; Multiple imputation; Two-step algorithm