Fitting conditional and simultaneous autoregressive spatial models in hglm

We present a new version (> 2.0) of the hglm package for fitting hierarchical generalized linear models (HGLMs) with spatially correlated random effects. CAR() and SAR() families for conditional and simultaneous autoregressive random effects were implemented. Eigen decomposition of the matrix describing the spatial structure (e.g., the neighborhood matrix) was used to transform the CAR/SAR random effects into an independent, but eteroscedastic, Gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR and SAR models. This gives a computationally efficient algorithm for moderately sized problems.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.