A resource selection model for analyzing pseudoreplicated data due to grouping behavior of animals

Quantifying resource selection is of primary interest in animal ecology. Many analyses of resource selection assume spatial and temporal independence of the sampling unit. Autocorrelation between observations, which is a general property of ecological variables, causes difficulties for most standard statistical procedures of resource selection because autocorrelated data violate the assumption of independence. To overcome this problem, we develop a mixed-effects model to estimate resource selection functions from data that are autocorrelated because of unobserved grouping behavior by animals. In the application of the expectation-maximization (EM) algorithm, the computation of the conditional expectation of the complete-data log-likelihood function does not have a closed-form solution requiring numerical integration. A Monte Carlo EM algorithm with Gibbs sampling can be used effectively in such situations to find exact maximum likelihood estimates. We propose a simple automated Monte Carlo EM algorithm with multiple sequences in which the Monte Carlo sample size is increased when the EM step is swamped by Monte Carlo errors.We demonstrate that the model can detect inherent autocorrelation and provide reasonable variance estimates when applied to nocturnal bird migration data. This approach could also be applied to ecological processes with various types of spatially and temporally autocorrelated data, circumventing serious problems caused by dangerous pseudoreplication.