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ANOVA models for Brownian motion

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  • Gordon Hazen
  • Daniel Apley
  • Neehar Parikh

Abstract

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.

Suggested Citation

  • Gordon Hazen & Daniel Apley & Neehar Parikh, 2017. "ANOVA models for Brownian motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7642-7660, August.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:15:p:7642-7660
    DOI: 10.1080/03610926.2016.1158834
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