Equivalence of Partial-Least-Squares SEM and the Methods of Factor-Score Regression. Issue 4 (4th July 2021) - Yuan, Ke-Hai; Deng, Lifang
ABSTRACT: Partial-least-squares approach to structural equation modeling (PLS-SEM) uses proxies of latent variables to conduct regression analysis, which directly addresses the needs of prediction and classification. Regression analysis using factor-scores has the same capacity but different factor scores have been noted with different properties. This article shows that different combinations of Bartlett- and regression-factor-scores are statistically equivalent in regression analysis for the purpose of prediction and parameter testing, and PLS-SEM mode B is equivalent to regression analysis using factor-scores when the model is correctly specified. Because proxies under PLS-SEM mode B enjoy the property of maximum reliability as that of factor-scores and PLS-SEM mode A enjoy numerical stability, a structure-based transformation from mode A to mode B is proposed. This transformation is expected to perform well for PLS-SEM in practice as long as the model has a relatively good fit to the data. Following the equivalence between factor-score regression and mode B of PLS-SEM, this article further proposes to use the maximum reliability coefficient as a formal measure for the goodness of PLS-SEM mode B and another consistent reliability coefficient for the goodness of mode A. The equivalence between PLS-SEM and the method of factor-score regression is examined via the analysis of a real dataset. A robust transformation technique is also introduced and illustrated for conducting empirical data analysis.