An evaluation of multi‐species occupancy models with correlated species occurrences

Abstract Multi‐species occupancy models for estimating the effects of environmental covariates on species occurrences while accounting for the effects of false‐negative errors in detection were developed more than 20 years ago. Only recently have these models been extended to include correlations in occurrence between species. Tobler et al. (2019) proposed two of these models wherein species occurrences are specified using a probit‐regression model of correlated multivariate binary outcomes. In one model, correlations in occurrence between species are formal parameters. In the other model, a factor‐analytic approximation of these correlations is used. After conducting extensive simulation studies to compare the performance of these models, Tobler et al. (2019) recommended the latter model in favour of the former owing to difficulties in fitting the former to simulated or real data. The same software (JAGS) was used to fit both models. Since the former model specifies the actual process used to generate species occurrences, we hypothesized that shortcomings in the software were responsible for the difficulties reported by Tobler et al. (2019). We therefore devised an efficient Markov chain Monte Carlo algorithm for fitting the data‐generating, multi‐species occupancy model using parameter‐expanded data augmentation. Using this algorithm, we conducted analyses of simulated data sets to re‐evaluate and compare the performance of the two multi‐species occupancy models. We also compared the results of fitting these models to a real dataset collected in camera‐trap surveys of mammalian species on the Tibetan Plateau. Our analyses of simulated data revealed that estimators of species occurrence, correlation and detection parameters had similar performance in terms of average bias, average root‐mean‐squared error and average coverage of 95% credible intervals regardless of whether the data‐generating model or its factor‐analytic approximation was used to analyse the data. However, our analyses also revealed the presence of systematic bias in the correlation estimates of both models, wherein strongly negative correlations were overestimated and strongly positive correlations were underestimated. Systematic bias was not evident in correlations estimated by fitting a multivariate probit regression model to latent species occurrences; therefore, the systematic bias in correlation estimates of the two occupancy models must have been produced by the failure of these models to estimate latent species occurrences accurately.