Graphical diagnostics for occupancy models with imperfect detection

Occupancy-detection models that account for imperfect detection have become widely used in many areas of ecology. As with any modelling exercise, it is important to assess whether the fitted model encapsulates the main sources of variation in the data, yet there have been few methods developed for occupancy-detection models that would allow practitioners to do so. In this paper, a new type of residual for occupancy-detection models is developed according to the method of Dunn & Smyth (Journal of Computational and Graphical Statistics, 5, 1996, 236–244). Residuals are separately constructed to diagnose the occupancy and detection components of the model. Because the residuals are quite noisy, we suggest fitting a smoother through plots of residuals against predictors of fitted values, with 95% confidence bands, to diagnose lack-of-fit. The method is illustrated using Swiss squirrel data, and evaluated using simulations based on that dataset. Plotting residuals against predictors or against fitted values performed reasonably well as methods for diagnosing violations of occupancy-detection model assumptions, particularly plots of residuals against a missing predictor. Relatively high false positive rates were sometimes observed, but this seems to be controlled reasonably well by fitting smoothers to these plots and being guided in interpretation by 95% confidence bands around the smoothers.