2015/01/26 by David C. Bardos, Gurutzeta Guillera‐Arroita, Bardos, David C. +3
Economics, Econometrics and Finance · Environmental Science · #62H11 #Ecology and Vegetation Dynamics Studies #Economic and Environmental Valuation #FOS: Biological sciences #FOS: Computer and information sciences #Methodology (stat.ME) #Quantitative Methods (q-bio.QM) #Species Distribution and Climate Change
paper · pdf · doi:10.48550/arxiv.1501.06530
openalex publication_date 2015/01/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The autologistic model and related auto-models, commonly applied as autocovariate regression, offer distinct advantages for analysing spatially autocorrelated ecological data. However, comparative studies by Carl and Kühn (Ecol. Model., 2007, 207, 159), Dormann (Ecol. Model., 2007, 207, 234), Dormann et al. (Ecography, 2007, 30, 609) and Beale et al. (Ecol. Lett., 2010, 13, 246) concluded that autocovariate regression yields anomalous covariate parameter estimates. The last three studies were based on erroneous numerical evidence, due to violation of conditions (Besag, J. R. Stat. Soc., Ser. B, 1974, 36, 192) for auto-model validity. Here we show that after correcting these technical errors, a more fundamental conceptual error remains: the comparative studies are founded on a mathematically incorrect notion of bias, involving direct comparison of parameter estimates across models differing in mathematical structure. We develop a set of simulation-based measures of covariate influence that are directly comparable across models and apply them to examples from the abovementioned studies. We find that in these cases, the effect of auto-model parameters is similar to (and consistent with) corresponding linear model effects, due to a phenomenon within auto-models that we refer to as "covariate amplification". Thus, simple comparison of parameter magnitudes between structurally different models can be highly misleading. We demonstrate that the recent critique of auto-models is entirely unfounded. Correctly applied and interpreted, autocovariate regression provides a practical approach to inference for spatially autocorrelated species distribution or abundance data, while overcoming well-known limitations of generalized linear models.