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Journal of Statistical Theory and Practice

, Volume 1, Issue 3–4, pp 311–328 | Cite as

Design for Hyperparameter Estimation in Linear Models

  • Qing Liu
  • Angela M. Dean
  • Greg M. Allenby
Article

Abstract

Optimal design for the joint estimation of the mean and covariance matrix of the random effects in hierarchical linear models is discussed. A criterion is derived under a Bayesian formulation which requires the integration over the prior distribution of the covariance matrix of the random effects. A theoretical optimal design structure is obtained for the situation where the random effects have equal variances and zero covariances. For other situations, optimal designs are obtained through computer search. It is shown that orthogonal designs, if they exist, are optimal under a main effects model with independent random effects. When the random effects are believed to be correlated, it is shown by example that nonorthogonal designs tend to be more efficient than orthogonal designs. In addition, design robustness is studied under various prior mean specifications of the random effects covariance matrix.

AMS 2000 subject classification

62K05 and 62K15 

Keywords

Bayesian Design Optimal Design Hierarchical Linear Model Hyperparameter Random Effects Model 

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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Department of MarketingUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of StatisticsThe Ohio State UniversityColumbusUSA
  3. 3.Department of MarketingThe Ohio State UniversityColumbusUSA

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