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Spatial generalized linear mixed models (SGLMMs) are popular for analyzingnon-Gaussian spatial data. These models assume a prescribed link function thatrelates the underlying spatial field with the mean response. There arecircumstances, such as when the data contain outlying observations, where theuse of a prescribed link function can result in poor fit, which can be improvedby using a parametric link function. Some popular link functions, such as theBox-Cox, are unsuitable because they are inconsistent with the Gaussianassumption of the spatial field. We present sensible choices of parametric linkfunctions which possess desirable properties. It is important to estimate theparameters of the link function, rather than assume a known value. To that end,we present a generalized importance sampling (GIS) estimator based on multipleMarkov chains for empirical Bayes analysis of SGLMMs. The GIS estimator,although more efficient than the simple importance sampling, can be highlyvariable when used to estimate the parameters of certain link functions. Usingsuitable reparameterizations of the Monte Carlo samples, we propose modifiedGIS estimators that do not suffer from high variability. We use Laplaceapproximation for choosing the multiple importance densities in the GISestimator. Finally, we develop a methodology for selecting models withappropriate link function family, which extends to choosing a spatialcorrelation function as well. We present an ensemble prediction of the meanresponse by appropriately weighting the estimates from different models. Theproposed methodology is illustrated using simulated and real data examples.

Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling