Abstract
Two important recent advances in areal modeling are the centered autologistic model and the sparse spatial generalized linear mixed model (SGLMM), both of which are reparameterizations of traditional models. The reparameterizations improve regression inference by alleviating spatial confounding, and the sparse SGLMM also greatly speeds computing by reducing the dimension of the spatial random effects. Package ngspatial ('ng' = non-Gaussian) provides routines for fitting these new models. The package supports composite likelihood and Bayesian inference for the centered autologistic model, and Bayesian inference for the sparse SGLMM.
Highlights
Background and introductionThe traditional autologistic model (Besag, 1972) and areal GLMM (Besag et al, 1991) have enjoyed widespread popularity: they have been applied thousands of times in many fields, e.g., epidemiology, marketing, agriculture, ecology, forestry, geography, and image analysis
The confounding of the mixed model was first addressed by Reich et al (2006) using a technique known as restricted spatial regression (Hodges and Reich, 2010). This technique alleviates spatial confounding and yields a faster mixing Markov chain, but the computational burden remains high because the dimension of the spatial random effects is reduced only slightly relative to the traditional model
By using the so called Moran operator, Hughes and Haran (2013) were able to reparameterize the mixed model in a way that improves regression inference and dramatically reduces the dimension of the random effects
Summary
Background and introductionThe traditional autologistic model (Besag, 1972) and areal GLMM (Besag et al, 1991) have enjoyed widespread popularity: they have been applied thousands of times in many fields, e.g., epidemiology, marketing, agriculture, ecology, forestry, geography, and image analysis. The resulting model, which we will call the sparse SGLMM, can be fitted so efficiently that even the largest areal datasets can be analyzed quickly. Package ngspatial supports composite likelihood and Bayesian inference for the centered autologistic model, and Bayesian inference for the sparse SGLMM.
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