Confidence regions for level differences in growth curve models

• Stochastic representation of maximum likelihood estimator of level differences.
• Confidence regions for level differences under normality.
• Confidence regions for level differences under nonnormality with finite correction.
• Real data illustration and geometrical explanations are provided.

In a pre-post or other kind of repeated measures study, it is sometimes clear that the mean profiles of the repeated measures are parallel across treatment groups. When for example, it can be assumed that there is no interaction between the repeated measure factor and the treatment, it would be of interest to know how much of a difference exists in the effect of the treatments. Such differences in the absence of interaction are referred to as level differences. In this paper, we consider methods for constructing confidence regions for level differences in the multi-dimensional cases. We derive asymptotic expansions for some intuitively appealing pivotal quantities to construct the confidence regions corrected up to the second order. Such corrections are shown in the multivariate literature to improve the accuracy of asymptotic approximations. We evaluate the finite sample performance of the confidence regions via a simulation study. Real-data example from forestry is used to provide an empirical illustration of the features of the various confidence regions proposed in the paper.