  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 K\"uhn
(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.
