Auto-logistic and related auto-models, implemented approximately as
autocovariate regression, provide simple and direct modelling of spatial
dependence. The autologistic model has been widely applied in ecology since
Augustin, Mugglestone and Buckland (J. Appl. Ecol., 1996, 33, 339) analysed red
deer census data using a hybrid estimation approach, combining maximum
pseudo-likelihood estimation with Gibbs sampling of missing data. However
Dormann (Ecol. Model., 2007, 207, 234) questioned the validity of auto-logistic
regression, giving examples of apparent underestimation of covariate parameters
in analysis of simulated "snouter" data. Dormann et al. (Ecography, 2007, 30,
609) extended this analysis to auto-Poisson and auto-normal models, reporting
similar anomalies. All the above studies employ neighbourhood weighting schemes
inconsistent with conditions (Besag, J. R. Stat. Soc., Ser. B, 1974, 36, 192)
required for auto-model validity; furthermore the auto-Poisson analysis fails
to exclude cooperative interactions. We show that all "snouter" anomalies are
resolved by correct auto-model implementation. Re-analysis of the red deer data
shows that invalid neighbourhood weightings generate only small estimation
errors for the full dataset, but larger errors occur on geographic subsamples.
A substantial fraction of papers applying auto-logistic regression to
ecological data use these invalid weightings, which are default options in the
widely used "spdep" spatial dependence package for R. Auto-logistic analyses
using invalid neighbourhood weightings will be erroneous to an extent that can
vary widely. These analyses can easily be corrected by using valid
neighbourhood weightings available in "spdep". The hybrid estimation approach
for missing data is readily adapted for valid neighbourhood weighting schemes
and is implemented here in R for application to sparse presence-absence data.Comment: Typos corrected in Table 1. Note that defaults in R package 'spdep'
have changed in response to this paper; some results using defaults are
therefore now version-dependen
