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On the Correlation Structure of Gaussian Copula Models for Geostatistical Count Data

期刊

出版社

WILEY
DOI: 10.1111/anzs.12140

关键词

Frechet-Hoeffding upper bound; Gaussian random field; isotropy; negative binomial; Poisson-Gamma model; zero-inflated Poisson

资金

  1. U.S. National Science Foundation [DMS-1208896]
  2. Division Of Mathematical Sciences
  3. Direct For Mathematical & Physical Scien [1208896] Funding Source: National Science Foundation

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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.

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