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Biometrika 1999 86(2):289-300; doi:10.1093/biomet/86.2.289
© 1999 by Biometrika Trust
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Orthogonality and transformations in variance components models

PJ SolomonA1 and JMG TaylorA2

A1 Department of Statistics, University of Adelaide, Adelaide, South Australia 5005 E-mail: psolomon@stats.adelaide.edu.au A2 Department of Biostatistics, University of Michigan, 1420 Washington Height, Ann Arbor, Michigan 48109, USA E-mail: jmgt@umich.edu

We consider variance components and other models for repeated measures in which a general transformation is applied to the response variable. Using Cox & Reid's (1987) concept of parameter orthogonality and some approximations to the information matrix we show that the intraclass correlation coefficient in the one-way model is robust to the choice of transformation. This robustness result generalises to a vector of parameters determining the correlation structure, to more complex variance components models, to multivariate normal models, to some longitudinal models and models involving linear regression functions, for which we show that ratios of regression parameters are robustly estimated. The results suggest that a natural way to parameterise the covariance structure in repeated measures models may be in terms of the variance and the correlation determined by separate sets of parameters.

Key Words: Intraclass correlation; Longitudinal data; Parameter orthogonality; Power transformation; Repeated measures; Variance components.


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