ANOVA models for Brownian motion

Gordon B Hazen*, Daniel Apley, Neehar Parikh

*Corresponding author for this work

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)7642-7660
Number of pages19
JournalCommunications in Statistics - Theory and Methods
Volume46
Issue number15
DOIs
StatePublished - Aug 3 2017

Fingerprint

Brownian motion
Tables
Tumor Growth
Fixed Effects
Covariance Structure
Random Effects
Model
Linear Model
Sample Size
Closed-form

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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ANOVA models for Brownian motion. / Hazen, Gordon B; Apley, Daniel; Parikh, Neehar.

In: Communications in Statistics - Theory and Methods, Vol. 46, No. 15, 03.08.2017, p. 7642-7660.

Research output: Contribution to journalArticle

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AU - Apley, Daniel

AU - Parikh, Neehar

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AB - 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.

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