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December 1999 Balance and orthogonality in designs for mixed classification models
David S. Birkes, Justus F. Seely, Dawn M. Vanleeuwen
Ann. Statist. 27(6): 1927-1947 (December 1999). DOI: 10.1214/aos/1017939245


A classification model is easiest to analyze when it has a balanced design. Many of the nice features of balanced designs are retained by error-orthogonal designs, which were introduced in a recent paper by the authors. The present paper defines a kind of ‘‘partially balanced’’ design and shows that this partial balance is sufficient to ensure the error-orthogonality of a mixed classification model. Results are provided that make the partial balance condition easy to check. It is shown that, for a maximal-rank error-orthogonal design, the Type I sum of squares for a random effect coincides with the Type II sum of squares.


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David S. Birkes. Justus F. Seely. Dawn M. Vanleeuwen. "Balance and orthogonality in designs for mixed classification models." Ann. Statist. 27 (6) 1927 - 1947, December 1999.


Published: December 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0963.62059
MathSciNet: MR1765623
Digital Object Identifier: 10.1214/aos/1017939245

Primary: 62J10
Secondary: 62K99

Keywords: ANOVA , mixed linear model , orthogonal block structure , orthogonal design , sums of squares

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 6 • December 1999
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