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 ...

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Patrick O. Perry, Art B. Owen
• Keywords: Gaussian Background Noise, JMLR 2010, Latent Variables, Multivariate Regression Context