Goodness-of-fit tests for spatial capture-recapture

Spatial capture recapture is used to estimate animal density and provide inferences on ecological and sampling factors affecting animal populations and observations. However, the assumptions of spatial capture recapture are rarely checked for the data at hand. Prior to this thesis, existing goodness-of-fit tests for SCR were largely restricted to Bayesian methods and therefore inaccessible to practitioners using frequentist methods whilst also being difficult to assess via simulations. It was also unclear what aspects of model fit were being tested by the goodness-of-fit tests and what could be done to improve the model. In this thesis, we aim to increase the accessibility and utility of goodness-of-fit tests for spatial capture-recapture. In Chapter 2, we develop a Monte Carlo resampling approach that allows us to imitate the conditioning of Bayesian goodness-of-fit tests on animal activity centres in frequentist spatial capture recapture models, thus allowing these tests to be used by both frequentist and Bayesian practitioners. We also use simulations to study the power and diagnostic abilities of these tests to understand the extent of their capabilities. In Chapter 3, we investigate if the aspects of model fit measured by the goodness-of-fit tests are correlated with bias in spatial capture-recapture parameters. We infer if goodness-of-fit tests are able to predict bias in spatial capture-recapture model estimates using a linear mixed effects model. In Chapter 4, we attempt to improve a goodness-of-fit test for individual heterogeneity. We hypothesise that conditioning fit statistics on activity centres as seen in Chapter 2 results in reduced power to detect lack-of-fit from unmodelled individual heterogeneity. We propose a resampling approach that marginalises across activity centre locations and resamples from the full model instead. Through our research, we extend the applicability of goodness-of-fit tests across different inferential paradigms and gain a better understanding of their characteristics.