ANOVA models for Brownian motion

Gordon Hazen; Daniel Apley; Neehar Parikh

doi:10.1080/03610926.2016.1158834

ANOVA models for Brownian motion

Gordon Hazen^*, Daniel Apley, Neehar Parikh

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	7642-7660
Number of pages	19
Journal	Communications in Statistics - Theory and Methods
Volume	46
Issue number	15
DOIs	https://doi.org/10.1080/03610926.2016.1158834
State	Published - Aug 3 2017

Keywords

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

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610926.2016.1158834

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title = "ANOVA models for Brownian motion",

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.",

keywords = "ANOVA, Analysis of variance, Brownian motion, longitudinal models, random effects, stochastic heterogeneous tumor growth",

author = "Gordon Hazen and Daniel Apley and Neehar Parikh",

note = "Publisher Copyright: {\textcopyright} 2017 Taylor & Francis Group, LLC.",

year = "2017",

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doi = "10.1080/03610926.2016.1158834",

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T1 - ANOVA models for Brownian motion

AU - Hazen, Gordon

AU - Apley, Daniel

AU - Parikh, Neehar

PY - 2017/8/3

Y1 - 2017/8/3

N2 - 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.

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.

KW - ANOVA

KW - Analysis of variance

KW - Brownian motion

KW - longitudinal models

KW - random effects

KW - stochastic heterogeneous tumor growth

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M3 - Article

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EP - 7660

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 15

ER -

ANOVA models for Brownian motion

Abstract

Keywords

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