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On Rigorous Specification of ICAR Models

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  • Michael L. Lavine
  • James S. Hodges

Abstract

Intrinsic (or improper) conditional autoregressions, or ICARs, are widely used in spatial statistics, splines, dynamic linear models, and elsewhere. Such models usually have several variance components, including one for errors and at least one for random effects. Likelihood and Bayesian inference depend on the likelihood function of those variances. But in the absence of constraints or further specifications that are not inherent to ICARs, the likelihood function is arbitrary and thus so are some inferences. We suggest several ways to add constraints or further specifications, but any choice is merely a convention.

Suggested Citation

  • Michael L. Lavine & James S. Hodges, 2012. "On Rigorous Specification of ICAR Models," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 42-49, February.
    • Handle: RePEc:taf:amstat:v:66:y:2012:i:1:p:42-49
    DOI: 10.1080/00031305.2012.654746
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    References listed on IDEAS

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    1. Brian J. Reich & James S. Hodges & Vesna Zadnik, 2006. "Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease-Mapping Models," Biometrics, The International Biometric Society, vol. 62(4), pages 1197-1206, December.
    2. Taraldsen, Gunnar & Lindqvist, Bo Henry, 2010. "Improper Priors Are Not Improper," The American Statistician, American Statistical Association, vol. 64(2), pages 154-158.
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    Cited by:

    1. Ferreira, Marco A.R. & Porter, Erica M. & Franck, Christopher T., 2021. "Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    2. Thomas Kneib & Nadja Klein & Stefan Lang & Nikolaus Umlauf, 2019. "Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-39, March.

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