Estimation of Unattenuated Factor Loadings

It is demonstrated that traditional exploratory factor analytic methods, when applied to correlation matrices, cannot be used to estimate unattenuated factor loadings. However, these values can be accurately estimated when the disattenuated correlation matrix, or the covariance matrix, is used as input. A mathematical basis for the advantage of this application of factor analysis is presented in this paper, as is an explanation of how these equations apply differentially to common factor analysis (CFA) and principal component analysis (PCA). Graphic displays which describe the comparative performance of CFA and PCA when extracting factors from the correlation matrix, the covariance matrix, and the disattenuated correlation matrix are provided. It is concluded that although the most accurate estimates of the unattenuated factor loadings can be achieved when CFA is used to decompose the covariance matrix or the disattenuated correlation matrix as the percentage of measurement error decreases, and the number of indicators per factor increases, the impact of methodology choice diminishes.