An Asymmetric Approach to Multiple‐factor Analysis

After a brief history of asymmetric approaches in factor analysis and related fields, there is derived a new asymmetric procedure that avoids communality estimation and other difficulties. This new solution splits a test battery 1 into sub‐batteries x and y , each of which spans the same factor space as does a test battery 2. This permits finding the unknown transformation that converts any factorization of the between‐battery correlations R 12 into an orthogonal factor matrix reproducing both R 12 and R xy , the between‐sub‐battery correlations.