Variable selection and accurate predictions in habitat modelling: a shrinkage approach

Habitat modelling is increasingly relevant in biodiversity and conservation studies. A typical application is to predict potential zones of specific conservation interest. With many environmental covariates, a large number of models can be investigated but multi-model inference may become impractical. Shrinkage regression overcomes this issue by dealing with the identification and accurate estimation of effect size for prediction. In a Bayesian framework we investigated the use of a shrinkage prior, the Horseshoe, for variable selection in spatial generalized linear models (GLM). As study cases, we considered 5 datasets on small pelagic fish abundance in the Gulf of Lion (Mediterranean Sea, France) and 9 environmental inputs. We compared the predictive performances of a simple kriging model, a full spatial GLM model with independent normal priors for regression coefficients, a full spatial GLM model with a Horseshoe prior for regression coefficients and 2 zero-inflated models (spatial and non-spatial) with a Horseshoe prior. Predictive performances were evaluated by cross-validation on a hold-out subset of the data: models with a Horseshoe prior performed best, and the full model with independent normal priors worst. With an increasing number of inputs, extrapolation quickly became pervasive as we tried to predict from novel combinations of covariate values. By shrinking regression coefficients with a Horseshoe prior, only one model needed to be fitted to the data in order to obtain reasonable and accurate predictions, including extrapolations.