Orthogonality and transformations in variance components models

In this paper we consider variance components and other models for repeated measures in which a general transformation is applied to the response variable. Using Cox and Reid's concept of parameter orthogonality (1987, JRSS B 49, 1-18) and some approximations to the information matrix we show that the intraclass correlation coe cient 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. The results suggest a natural way to parametrise the covariance structure in repeated measures models is in terms of the variance and the correlation determined by separate sets of parameters.