Estimation of unattenuated factor loadings

It is demonstrated that traditional exploratory factor analytic methods, wh en applied to correlation matrices, cannot be used to estimate unattenuated factor loadings. However these values can be accurately estimated when the disattenuated correlation matrix, ol the covariance mat,ix, is used as inp ut. A mathematical basis for the advantage of this application of factor. a nalysis is presented in this paper as is an explanation of how these equati ons apply differentially To common factor analysis (CFA) and principal comp onent analysis (PCA). Graphic displays which describe the comparative perfo rmance of CFA and PCA when extracting factors from the correlation matrix, the covariance matrix, and the disattenuated correlation matrix ale provide d. It is concluded that although the most accurate estimates of the unatten uated factor loadings can be achieved when CFA is used to decompose the cov ariance matrix or the disattenuated correlation matrix as the percentage of measurement error decreases, and the number of indicators per factor incre ases, the impact of methodology choice diminishes.