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Biostatistics Advance Access published online on January 30, 2007
Biostatistics, doi:10.1093/biostatistics/kxm003
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Identifying Latent Clusters of Variability in Longitudinal Data

Michael R. Elliott1,2

1 Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI 48109
2 Institute for Social Research, University of Michigan, 426 Thompson Street, Ann Arbor, MI 48106

email: mrelliot{at}umich.edu. Telephone: (734) 647-5160; Fax: (734) 763-2215.

Means or other central tendency measures are by far the most common focus of statistical analyses. However, as Carroll (2003) noted, "systematic dependence of variability on known factors" may be "fundamental to the proper solution of scientific problems" in certain settings. We develop a latent cluster model that relates underlying "clusters" of variability to baseline or outcome measures of interest. Because estimation of variability is inextricably linked to estimation of trend, assumptions about underlying trends are minimized by using nonparametric regression estimates. The resulting residual errors are then clustered into unobserved clusters of variability that are in turn related to subject-level predictors of interest. An application is made to psychological affect data.

Keywords: Variance function; heteroscedasticity; cubic spline; nonparametric regression; longitudinal profiles

Received May 9, 2006; revised December 13, 2006; accepted for publication January 23, 2007.


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