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Abstract:
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Techniques for estimating relationships between a spatially indexed response and a set of covariates are well-known when the response can be assumed Gaussian. For a discrete response, some authors have adapted Liang and Zeger's (1986) generalized estimating equations approach. These models typically employ a spatially correlated latent variable. Latent variable models place artificially low limits on correlations, which can lead to underestimating standard errors. I propose a copula-based maximum likelihood approach for spatially correlated discrete data. This approach allows modeling of correlations up to the theoretical limit, and, given appropriate regularity conditions, enjoys all the nice properties of maximum likelihood. The proposed method can be applied to any correlated non-Gaussian data including time series, space-time problems, and longitudinal data.
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