A Rotation Test to Verify Latent Structure

9 years 5 months ago
A Rotation Test to Verify Latent Structure
We consider here how to tell whether a latent variable that has been estimated in a multivariate regression context might be real. Often a followup investigation will find a real physical variable that corresponds closely to the latent variable and that will settle the issue. If no such variable is uncovered then a statistical test for whether the variable is real is desirable. It is well known that a Gaussian latent variable cannot be identified in the presence of Gaussian background noise. But a nonGaussian variable can be distinguished from such noise. Instead of testing based on the magnitude of the latent variable, we test based on a measure of its non-Gaussianity, via a projection pursuit criterion. To judge the statistical significance of the observed criterion, we introduce a test based on uniform random rotations of the data, taken in a space orthogonal to the measured regression variables. For the microarray data of the AGEMAP consortium, we confirm the presence of some ...
Patrick O. Perry, Art B. Owen
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JMLR
Authors Patrick O. Perry, Art B. Owen
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