Two-stage approaches to the analysis of occupancy data I: the homogeneous case (analysis of occupancy data)

Abstract

Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show that for the homogeneous occupancy model there is an orthogonal transformation of the parameters that gives a natural two-stage inference procedure based on a conditional likelihood. We then extend this to a partial likelihood that gives explicit estimators of the model parameters. By allowing the separate modelling of the detection and occupancy probabilities, the extension of the two-stage approach to more general models has the potential to simplify the computational routines used there.

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

“…In Karavarsamis and Huggins (2017) we examined the two-stage approach for the homogeneous occupancy model. Here we examined 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 results from conditioning on at least one detection. However, when the main focus is on estimating occupancy, the occupancy probability appears to be relatively insensitive for small changes in detection probability (Karavarsamis and Huggins, 2017).…”

“…Following the homogeneous case of Karavarsamis and Huggins (2017) an alternate approach is to let η s (= ψ s θ s ) be the unconditional probability the species is detected at site s. Then we may write the contribution of site s to the full likelihood, (1), as…”

“…For the homogeneous model Karavarsamis and Huggins (2017) included in their supplementary materials a plot of the estimated occupancy probability against values of the detection probability. This plot suggests that the occupancy probability is relatively insensitive to small changes in the detection probability.…”

“…Recently Karavarsamis and Huggins (2017) showed that for the homogeneous occupancy model a simple transformation yielded orthogonal parameters resulting in a two-stage estimation procedure that simplified the computation of the estimates. We see in Section 3 that this no longer holds for heterogeneous models.…”