Right-Censored Mixed Poisson Count Models with Detection Times

Conducting complete surveys on flora and fauna species within a sampling unit (or quadrat) of interest can be costly, particularly if there are several species in high abundance. A commonly used approach, which aims to reduce time and costs, consists of occurrence data reflecting the status of occupancy of a species– e.g., rather than counting every individual, the survey is stopped as soon as one individual has been observed. Although this approach is cheaper to conduct than a complete survey, some statistical efficiency in model estimators is lost. In this study, we consider occurrence data as a special case of right-censored count data where the collecting process stops until some set threshold on the number of observed individuals is reached. We then propose a new class of regression estimation models for right-censored count data that incorporate information from detection times (or catch effort) collected during sampling. First, we show that incorporating ancillary information in the form of detection times can greatly improve statistical efficiency over, say, right-censored Poisson or negative binomial models. Furthermore, the proposed models retain the same cost-effectiveness as censored-type models. We also consider zero-truncated and zero-inflated models for a variety of count data types. These models can be extended to a more general class of mixed Poisson models. We investigate model performance on simulated data and give two examples consisting of plant abundance data and bat acoustics data. Supplementary materials accompanying this paper appear online.