Confronting Imperfect Detection: Behavior of Binomial Mixture Models under Varying Circumstances of Visits, Sampling Sites, Detectability, and Abundance, in Small-Sample Situations

Abstract Binomial mixture models (BMMs) have been increasingly applied to account for imperfect detection and to estimate abundance from count data, but their performance has not been thoroughly evaluated. Here, I conducted simulation experiments to examine parameter estimates in BMMs under various situations. I generated data by assuming that abundance followed a Poisson distribution with an expected value &lgr; and that the number of detected individuals followed a binomial distribution with an individual detection probability p. In simple simulations without covariates for &lgr; and p, when the number of sampling sites (n) was between 20 and 160, BMMs could recover &lgr; and p under the following conditions: 0.1≤&lgr;≤160 and p≥0.1. However, within these ranges of &lgr; and p, the estimates were variable under lower values of &lgr; and p, although the situation improved as n increased. When &lgr; and p are expected to exceed these ranges and the sample size is small, the results suggest that sampling and/or modeling designs should be reconsidered. I then conducted simulation experiments with covariates. I assumed that &lgr; increased with a covariate (x) across 20 sampling sites. I varied p, number of visits (v), and their dependency on a covariate. To compare BMMs with analyses that did not accommodate imperfect detection, I fitted ordinary Poisson generalized linear models to mean and maximum counts (GLMmean and GLMmax). The results showed that GLMmax was superior to GLMmean because GLMmean underestimated &lgr; when p was small. GLMmax underestimated a coefficient of the covariate (slope) when v was negatively correlated with x. BMMs successfully recovered true values of the intercepts, slopes, and &lgr; in most cases. However, when p and v were small, and when p and &lgr; were highly negatively correlated due to their inverse dependency on x, estimates from BMMs were more variable.