ANOVA models for Brownian motion

Gordon Hazen*, Daniel Apley, Neehar Parikh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)7642-7660
Number of pages19
JournalCommunications in Statistics - Theory and Methods
Issue number15
StatePublished - Aug 3 2017


  • Analysis of variance
  • Brownian motion
  • longitudinal models
  • random effects
  • stochastic heterogeneous tumor growth

ASJC Scopus subject areas

  • Statistics and Probability


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