ANOVA models for Brownian motion

We investigate longitudinal models having Brownian-motion covariance structure. We show that any such model can be viewed as arising from a related timeless classical linear model where sample sizes correspond to longitudinal observation times. This relationship is of practical impact when there are closed-form ANOVA tables for the related classical model. Such tables can be directly transformed into the analogous tables for the original longitudinal model. We in particular provide complete results for one-way fixed and random effects ANOVA on the drift parameter in Brownian motion, and illustrate its use in estimating heterogeneity in tumor growth rates.