Orthogonality and transformations in variance components models

We consider variance components and other models for repeated measures in w hich a general transformation is applied to the response variable. Using Co x & Reid's (1987) concept of parameter orthogonality and some approximation s to the information matrix we show that the intraclass correlation coeffic ient in the one-way model is robust to the choice of transformation. This r obustness result generalises to a vector of parameters determining the corr elation structure, to more complex variance components models, to multivari ate normal models, to some longitudinal models and models involving linear regression functions, for which we show that ratios of regression parameter s are robustly estimated. The results suggest that a natural way to paramet erise the covariance structure in repeated measures models may be in terms of the variance and the correlation determined by separate sets of paramete rs.