Abstract #301786

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JSM 2003 Abstract #301786
Activity Number: 248
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #301786
Title: SVD Models for Cross-Covariance
Author(s): Jacob A. Wegelin*+ and Thomas Richardson
Companies: University of California, Davis and University of Washington
Address: Dept. of Epidemiology and Preventive Med-TB-168, Davis, CA, 95616,
Keywords: singular value decomposition ; behavioral teratology ; structural equation models ; latent variables ; partial least squares ; PLS
Abstract:

Suppose we have two blocks of measurements on 500 mother-child dyads: a questionnaire administered to the mother during pregnancy regarding alcohol consumption, and a battery of IQ subtests administered to the child at age seven. We wish to model the relationship between these observed variables and two variables not measured directly: the fetus's alcohol exposure and the neuroanatomical changes associated with this exposure and with IQ deficits. We specify a class of Gaussian models with latent variables for this problem. We show that any variance-covariance matrix for the observed variables satisfying a certain rank constraint on the covariance between the blocks can be induced by a model of this class. A parallel exists between this model and the singular value decomposition, providing an alternate construction of the model from the variance-covariance matrix, a precise characterization of the degree to which the model is under-identified, precise bounds on the correlation between the latent variables, and a stable, computationally inexpensive way to estimate coefficients. We discuss an extension of the model which permits multiple latent variables associated with each block.

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