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Activity Number:
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378
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Type:
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Contributed
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Date/Time:
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Wednesday, August 9, 2006 : 8:30 AM to 10:20 AM
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Sponsor:
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Biometrics Section
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| Abstract - #307291 |
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Title:
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Unconstrained Models for the Covariance Structure of Multivariate Longitudinal Data
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Author(s):
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Chulmin Kim*+ and Dale Zimmerman
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Companies:
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University of Minnesota, Morris and The University of Iowa
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Address:
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704 Imperial Drive, #309, Morris, MN, 56267,
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Keywords:
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multivariate longitudinal ; covariance matrix ; unconstrained parameterization ; Cholesky decomposition ; antedependence ; maximum likelihood estimators
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Abstract:
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The constraint that a covariance matrix must be positive definite presents difficulties for modeling its structure. In a series of papers published in 1999 and 2000, Mohsen Pourahmadi proposed a parameterization of the covariance matrix for univariate longitudinal data in which the parameters are unconstrained. This unconstrained parameterization is based on the modified Cholesky decomposition of the inverse of the covariance matrix. We extend this idea to multivariate longitudinal data. We develop a modified Cholesky block decomposition that provides an unconstrained parameterization for the covariance matrix. A Newton-Raphson algorithm is developed for obtaining maximum likelihood estimators of model parameters. The results along with penalized likelihood criteria such as BIC for model selection are illustrated using a real multivariate longitudinal dataset and a simulated data set.
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