On browne's solution for oblique procrustes rotation

Browne [1967] has given a method of solving the problem (originally stated by Mosier, [1939]) of finding a least squares fit to a specified factor structure. The problem is one of minimizing the sum of squared residuals of —FT with Diag (T'T)=I. Browne's solution involves the eigenvectors and values ofF'F and leads to an iterative solution.This paper gives a form of the solution which does not involve solution of an eigenvalue problem but does require an iteration similar to Browne's. It suggests the possible existence of a singularity, and a simple modification of Browne's computational procedure is proposed which deals with this case. A better starting value for the iteration is also proposed for which convergence is guaranteed using the ordinary Newton iteration.Part of this work was presented at the April 1969 meetings of the Psychometric Society. The anthor is indebted to Dr. Ledyard Tucker for some helpful discussions. This work was supported in part by a PHS Research Grant No. MH-10006 from the National Institute of Mental Health, and Grant No. GM-12868 from the Institute of General Medical Sciences, Public Health Service.