Estimating Occupancy and Fitting Models with the Two-Stage Approach

Abstract

The two-stage approach for occupancy modelling applies the partial and conditional likelihood to occupancy data and is an alternative to direct maximisation of the full likelihood that involves simultaneous estimation of occupancy and detection probabilities. The two-stage approach resolves limitations with the full likelihood and allows full use of GLM (generalised linear model) and GAM (generalised additive model) computing functions in standard software such as R. It reduces computation time as it significantly reduces the number of models to be assessed in model selection. The two-stage approach makes it easy to include covariates for heterogeneous GLMs and GAMs and we present these models for time dependent detection probabilities. For the basic occupancy model we provide complete solutions for maximum likelihood estimation at the boundaries of the sample space, where the score equations do not apply. We describe a region based on a convex hull within which estimates are certain to exist and evaluate the bias of the occupancy estimator.