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Dispersion matrix in balanced mixed ANOVA models

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
382
Identifiers
DOI: 10.1016/j.laa.2003.12.011
Keywords
  • Balanced Data
  • Inversed Dispersion Matrices
  • Mixed Linear Model
  • Variance Components

Abstract

Abstract The inverse of the dispersion matrix plays an important role in mixed model analysis. Searle and Henderson [J. Amer. Statist. Assoc, 74 (1979) 465] showed that for a general balanced mixed ANOVA model, such an inverse can be expression in the same form as the dispersion matrix, i.e., a linear combination of Kronecker products. However, the coefficients of such a linear combination are given in a way that it is not easy to see what each coefficient is. In this paper, we give explicit expressions for these coefficients. An application of the result is considered.

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