Two-stage approaches to the analysis of occupancy data II. The heterogeneous model and conditional likelihood

Abstract

Occupancy models involve both the probability a site is occupied and the probability occupancy is detected. The homogeneous occupancy model, where the occupancy and detection probabilities are the same at each site, admits an orthogonal parameter transformation that yields a two-stage process to calculate the maximum likelihood estimates. In this two-stage approach it is not necessary to simultaneously estimate the occupancy and detection probabilities. We examine the two-stage approach for the heterogeneous occupancy model where the occupancy and detection probabilities now depend on covariates that may vary between sites and over time. This effectively reduces the parameter space, allows the use of existing vector generalised linear models methods to fit models for detection and allows the development of an iterative weighted least squares approach to fit models for occupancy. Efficiency is examined in a simulation study and the full maximum likelihood and two-stage approaches are compared on several data sets.