We describe a class of random field models for geostatistical count data based on Gaussian copulas. Unlike hierarchical Poisson models often used to describe this type of data, Gaussian copula models allow a more direct modelling of the marginal distributions and association structure of the count data. We study in detail the correlation structure of these random fields when the family of marginal distributions is either negative binomial or zero-inflated Poisson; these represent two types of overdispersion often encountered in geostatistical count data. We also contrast the correlation structure of one of these Gaussian copula models with that of a hierarchical Poisson model having the same family of marginal distributions, and show that the former is more flexible than the latter in terms of range of feasible correlation, sensitivity to the mean function and modelling of isotropy. An exploratory analysis of a dataset of Japanese beetle larvae counts illustrate some of the findings. All of these investigations show that Gaussian copula models are useful alternatives to hierarchical Poisson models, specially for geostatistical count data that display substantial correlation and small overdispersion.
This work describes the R package gcKrig for the analysis of geostatistical count data using Gaussian copulas. The package performs likelihood-based inference and spatial prediction using Gaussian copula models with discrete marginals. Two different classes of methods are implemented to evaluate/approximate the likelihood and the predictive distribution. The package implements the computationally intensive tasks in C++ using an R/C++ interface, and has parallel computing capabilities to predict the response at multiple locations simultaneously. In addition, gcKrig also provides functions to simulate and visualize geostatistical count data, and to compute the correlation function of the counts. It is designed to allow a flexible specification of both the marginals and the spatial correlation function. The principal features of the package are illustrated by three data examples from ecology, agronomy and petrology, and a comparison between gcKrig and two other R packages.
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