An Empirical Comparison Of The Similarity Of Principal Component, Image, And Factor Patterns

Factor analysis, image component analysis, and principal component analysis are three methods that have been employed for the same purpose. Factor analysis was traditionally viewed as the preferred method, with other methods serving as computationally easier approximations. Recently attention has been focused on theoretical problems with the factor analysis model such as the factor indeterminacy issue. In order to assess the degree of similarity between the results produced by each of the three methods, the patterns produced by maximum likelihood factor analysis, rescaled image analysis, and principal component analysis are compared for nine data sets. Two different comparisons are considered: a direct loading-by-loading comparison of the patterns, and a summary statistic defined on the matrix of differences between patterns. Comparisons are made for the patterns in both orthogonal and oblique rotational positions, and a position of maximum similarity is achieved by an orthogonal procrustes rotation. The patterns produced by each of the three methods were remarkably similar. Image component analysis and maximum likelihood factor analysis generally produced the most similar results and principal component analysis and maximum likelihood factor analysis generally produced the most dissimilar results. Differences generally occurred in the last factor extracted, possibly because too many factors had been extracted.