Mixed effect models in distance sampling

Abstract

Recently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the design-based approach with a model-based approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003). While these models have generally been limited to include fixed effects, we propose four different methods for analysing distance sampling data using mixed effects models. These include an extension of the two-stage approach (Buckland et al., 2009), where we include site random effects in the second-stage count model to account for correlated counts at the same sites. We also present two integrated approaches which include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all parameters. Furthermore, we develop a detection function model that incorporates random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a Metropolis-Hastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models. We analyse two case studies, both large-scale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from the extended two-stage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.