A Recommendation for Classical and Robust Factor Analysis

Considering the factor analysis methods (classical or robust), the data input (data or scaled data), and the running matrix (covariance or correlation) all together, there are 8 combinations. The objective of the study is to give a recommendation for classical and robust factor analysis. First, when the variables have different units, it is common to standardize the variables, and thus it is common to use the correlation matrix as the running matrix. Second, we need to explain the factors from the loading matrix. The entries of the loading matrix from the sample covariance matrix are not limited between 0 and 1, which makes the explanations of the factors hard. Third, we may not be able to compute the robust covariance matrix, and thus the robust correlation matrix of the original data, as the stocks data example illustrates. Consequently, we recommend classical and robust factor analysis using the correlation matrix of the scaled data as the running matrix for theoretical and computational reasons. The hbk data and the stock611 data illustrate our recommendation.