Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

Abstract

It has long been known that insufficient consideration of spatial autocorrelation leads to unreliable hypothesis‐tests and inaccurate parameter estimates. Yet, ecologists are confronted with a confusing array of methods to account for spatial autocorrelation. Although Beale et al. (2010) provided guidance for continuous data on regular grids, researchers still need advice for other types of data in more flexible spatial contexts. In this paper, we extend Beale et al. (2010)‘s work to count data on both regularly‐ and irregularly‐spaced plots, the latter being commonly encountered in ecological studies. Through a simulation‐based approach, we assessed the accuracy and the type I errors of two frequentist and two Bayesian ready‐to‐use methods in the family of generalized mixed models, with distance‐based or neighbourhood‐based correlated random effects. In addition, we tested whether the methods are robust to spatial non‐stationarity, and over‐ and under‐dispersion – both typical features of species distribution count data which violate standard regression assumptions. In the simplest of our simulated datasets, the two frequentist methods gave inflated type I errors, while the two Bayesian methods provided satisfying results. When facing real‐world complexities, the distance‐based Bayesian method (MCMC with Langevin–Hastings updates) performed best of all. We hope that, in the light of our results, ecological researchers will feel more comfortable including spatial autocorrelation in their analyses of count data.

A Landscape View of Agricultural Insecticide Use across the Conterminous US from 1997 through 2012

“…Spatial patterns in model residuals, in particular, can indicate that important patterns and processes are not sufficiently represented by models [58–60]. Numerous simulation studies have shown that the consequences of this form of model misspecification include biased parameter estimates and unreliable hypothesis tests [41,43–45,61]. Indeed, strong spatial autocorrelation in this study (Fig 2A–2C and 2E) was associated with considerably different parameter estimates for some variables.…”

“…A final option is to simply accept spatially or temporally autocorrelated model residuals. However, residual autocorrelation indicates lack of independence in statistical replicates, and can be accompanied by biased parameter estimates and unreliable hypothesis tests [40–45]. The general approach in this analysis was to compare the performance of six models that varied in how they did, or did not, deal with spatially and temporally structured residuals, and then to draw inferences based on a best model or set of best models.…”

Space‐time investigation of the effects of fishing on fish populations

“…, Beale et al. , Saas and Gosselin ). However, many ecological studies still ignore spatial and/or temporal dependence (Dormann ).…”

“…Moreover, space‐time models are important for the analysis of spatial data to reduce the risk of producing unreliable or inaccurate parameter estimates (Dormann , Beale et al. , Saas and Gosselin ). While data are becoming easier and cheaper to acquire, we rarely have data on all influential environmental variables.…”

“…The inclusion of spatial (or temporal) autocorrelation in the model provides a flexible way to account for factors not explicitly included in the model (Dormann , Beale et al. , Saas and Gosselin , Shelton et al. ).…”