Valid auto-models for spatially autocorrelated occupancy and abundance data

Spatially autocorrelated species abundance or distribution datasets typically generate spatially autocorrelated residuals in generalized linear models; a broader modelling framework is therefore required. 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 (Journal of Applied Ecology, 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 (Ecological Modelling, 2007, 207, 234) questioned the validity of auto-logistic regression even for fully-observed data, giving examples of apparent underestimation of covariate parameters in analysis of simulated ‘snouter’ data. Extending this critique to include auto-Poisson and uncentered auto-normal models, Dormann et al. (Ecography, 2007, 30, 609) found likewise that covariate parameters estimated via autocovariate regression bore little resemblance to values used to generate ‘snouter’ data. We note that all the above studies employ neighbourhood weighting schemes inconsistent with auto-model definitions; in the auto-Poisson case, a further inconsistency was the failure to exclude cooperative interactions. We investigate the impact of these implementation errors on auto-model estimation using both empirical and simulated datasets. We show that when ‘snouter’ data is reanalysed using valid weightings, very different estimates are obtained for covariate parameters. For auto-logistic and auto-normal models, the new estimates agree closely with values used to generate the ‘snouter’ simulations. 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 employing auto-logistic regression use these invalid neighbourhood weightings, which are embedded as default options in the widely used ‘spdep’ spatial dependence package for R. Auto-logistic analyses conducted 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.