Dimension reduction and alleviation of confounding for spatial generalized linear mixed models

John Hughes, Murali Haran

Research output: Contribution to journalArticlepeer-review

230 Scopus citations


Non-Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data, but this model suffers from two major shortcomings: variance inflation due to spatial confounding and high dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count and Gaussian spatial data sets, and to a large infant mortality data set.

Original languageEnglish (US)
Pages (from-to)139-159
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - Jan 1 2013


  • Dimension reduction
  • Generalized linear model
  • Harmonic analysis
  • Mixed model
  • Regression
  • Spatial statistics


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