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Characterizing the variance improvement in linear Dirichlet random effects models

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  • Kyung, Minjung
  • Gill, Jeff
  • Casella, George

Abstract

An alternative to the classical mixed model with normal random effects is to use a Dirichlet process to model the random effects. Such models have proven useful in practice, and we have observed a noticeable variance reduction, in the estimation of the fixed effects, when the Dirichlet process is used instead of the normal. In this paper we formalize this notion, and give a theoretical justification for the expected variance reduction. We show that for almost all data vectors, the posterior variance from the Dirichlet random effects model is smaller than that from the normal random effects model.

Suggested Citation

  • Kyung, Minjung & Gill, Jeff & Casella, George, 2009. "Characterizing the variance improvement in linear Dirichlet random effects models," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2343-2350, November.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:22:p:2343-2350
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    References listed on IDEAS

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    1. Robert M. Dorazio & Bhramar Mukherjee & Li Zhang & Malay Ghosh & Howard L. Jelks & Frank Jordan, 2008. "Modeling Unobserved Sources of Heterogeneity in Animal Abundance Using a Dirichlet Process Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 635-644, June.
    2. Gill, Jeff & Casella, George, 2009. "Nonparametric Priors for Ordinal Bayesian Social Science Models: Specification and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 453-454.
    3. Deborah Burr & Hani Doss, 2005. "A Bayesian Semiparametric Model for Random-Effects Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 242-251, March.
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    1. Minjung Kyung & Jeff Gill & George Casella, 2011. "Sampling schemes for generalized linear Dirichlet process random effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(3), pages 259-290, August.

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