Prior choice and data requirements of Bayesian multivariate hierarchical models fit to tag-recovery data: The need for power analyses

Abstract

Recent empirical studies have quantified correlation between survival and recovery by estimating these parameters as correlated random effects with hierarchical Bayesian multivariate models fit to tag-recovery data. In these applications, increasingly negative correlation between survival and recovery has been interpreted as evidence for increasingly additive harvest mortality. The power of these hierarchal models to detect nonzero correlations has rarely been evaluated, and these few studies have not focused on tag-recovery data, which is a common data type. We assessed the power of multivariate hierarchical models to detect negative correlation between annual survival and recovery. Using three priors for multivariate normal distributions, we fit hierarchical effects models to a mallard (Anas platyrhychos) tag-recovery data set and to simulated data with sample sizes corresponding to different levels of monitoring intensity. We also demonstrate more robust summary statistics for tag-recovery data sets than total individuals tagged. Different priors led to substantially different estimates of correlation from the mallard data. Our power analysis of simulated data indicated most prior distribution and sample size combinations could not estimate strongly negative correlation with useful precision or accuracy. Many correlation estimates spanned the available parameter space (-1,1) and underestimated the magnitude of negative correlation. Only one prior combined with our most intensive monitoring scenario provided reliable results. Underestimating the magnitude of correlation coincided with overestimating the variability of annual survival, but not annual recovery. The inadequacy of prior distributions and sample size combinations previously assumed adequate for obtaining robust inference from tag-recovery data represents a concern in the application of Bayesian hierarchical models to tag-recovery data. Our analysis approach provides a means for examining prior influence and sample size on hierarchical models fit to capture-recapture data while emphasizing transferability of results between empirical and simulation studies.

Keywords: Bayesian analysis; capture–recapture; harvest assessment; hierarchical models; multivariate normal distribution; random effects.