Sólymos, P., Lele, S. R. & Bayne, E. (2012): Conditional likelihood approach for analyzing single visit abundance survey data in the presence of zero inflation and detection error. Environmetrics 23: 197-205.
Current methods to correct for detection error require multiple visits to the same survey location. Many historical datasets exist that were collected using only a single visit, and logistical/cost considerations prevent many current research programs from collecting multiple visit data. In this paper, we explore what can be done with single visit count data when there is detection error. We show that when appropriate covariates that affect both detection and abundance are available, conditional likelihood can be used to estimate the regression parameters of a binomial–zero-inflated Poisson (ZIP) mixture model and correct for detection error. We use observed counts of Ovenbirds (Seiurus aurocapilla) to illustrate the estimation of the parameters for the binomial–zero-inflated Poisson mixture model using a subset of data from one of the largest and longest ecological time series datasets that only has single visits. Our single visit method has the following characteristics: (i) it does not require the assumptions of a closed population or adjustments caused by movement or migration; (ii) it is cost effective, enabling ecologists to cover a larger geographical region than possible when having to return to sites; and (iii) its resultant estimators appear to be statistically and computationally highly efficient.
closed populations, conditional likelihood, ecological monitoring, mixture models, open populations, pseudo-likelihood