Distance sampling with a random scale detection function

Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the half-normal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with long-tailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes (similar to 100) and compared the random scale half-normal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.