Testing environmental and genetic effects in the presence of spatial autocorrelation

Abstract

Spatial autocorrelation is a well‐recognized concern for observational data in general, and more specifically for spatial data in ecology. Generalized linear mixed models (GLMMs) with spatially autocorrelated random effects are a potential general framework for handling these spatial correlations. However, as the result of statistical and practical issues, such GLMMs have been fitted through the undocumented use of procedures based on penalized quasi‐likelihood approximations (PQL), and under restrictive models of spatial correlation. Alternatively, they are often neglected in favor of simpler but more questionable approaches. In this work we aim to provide practical and validated means of inference under spatial GLMMs, that overcome these limitations. For this purpose, a new software is developed to fit spatial GLMMs. We use it to assess the performance of likelihood ratio tests for fixed effects under spatial autocorrelation, based on Laplace or PQL approximations of the likelihood. Expectedly, the Laplace approximation performs generally slightly better, although a variant of PQL was better in the binary case. We show that a previous implementation of PQL methods in the R language, glmmPQL, is not appropriate for such applications. Finally, we illustrate the efficiency of a bootstrap procedure for correcting the small sample bias of the tests, which applies also to non‐spatial models.

The NATURA 2000 database as a tool in the analysis of habitat selection at large scales: factors affecting the occurrence of pine and stone martens in Southern Europe

“…The significance of fixed effects was estimated using a loglikelihood ratio test. The most common procedure used to deal with spatial autocorrelation is based on penalised quasilikelihood approximations (glmmPQL), but the assumptions underlying the autologistic regression used in this algorithm have been criticised recently (Betts et al, 2009;Rousset and Ferdy, 2014). Our preliminary analyses (results not reported) demonstrated that although penalised quasi-likelihood approximations produced similar results, the method suggested by Rousset and Ferdy (2014) was more conservative.…”

“…We plotted Moran's I autocorrelation coefficient calculated for pairs of spatial observations against distance (5 km increment) using the ncf package (R Development Core Team 2013). Rousset and Ferdy (2014) suggested accounting for this effect when inferring fixed effects, even if autocorrelation appears nonsignificant. Generalised linear mixed models (GLMMs) were applied with spatially autocorrelated random effects and a variant of penalised quasi-likelihood approximations (PQL/ L) for the estimation of fixed effects, as recommended for binary data (Rousset and Ferdy 2014).…”

“…Rousset and Ferdy (2014) suggested accounting for this effect when inferring fixed effects, even if autocorrelation appears nonsignificant. Generalised linear mixed models (GLMMs) were applied with spatially autocorrelated random effects and a variant of penalised quasi-likelihood approximations (PQL/ L) for the estimation of fixed effects, as recommended for binary data (Rousset and Ferdy 2014). The Matérn autocorrelation function was used to fit the random effect of spatial distances.…”

“…1.7.4-Wrocław (Szczepanek 2013). All statistical analyses were performed using R software (R Development Core Team 2013), package spaMM (Rousset and Ferdy 2014).…”

Automatic Object-Oriented, Spectral-Spatial Feature Extraction Driven by Tobler’s First Law of Geography for Very High Resolution Aerial Imagery Classification

“…Despite notable exceptions, it is hard to imagine a world in which the law is not true, and it provides a very useful principle for analyzing earth surface information [28]. The widespread application of geography today accommodates a variety of perspectives on the significance of this law [29,30]. Remote sensing imagery is obtained based on the radiance of specific source targets on the ground surface.…”