Statistical and Psychometric Properties of Three Weighting Schemes of the PLS-SEM Methodology

Structural equation modeling (SEM) is a widely used technique for studies involving latent constructs. While covariance-based SEMStructural Equation Model (SEM)covariance-based SEM (CBSEM) (CB-SEM)Covariance-Based SEM (CBSEM) permits estimating the regression relationship among latent constructs, the parameters governing this relationship do not apply to that among the scored values of the constructs, which are needed for prediction, classificationClassification and/or diagnosis of individuals/participants. In contrast, the partial-least-squares approach to SEM (PLS-SEM) first obtains weighted composites for each case and then estimates the structural relationship among the composites. Consequently, PLS-SEM is a preferred method in predicting and/or classifying individuals. Nevertheless, properties of PLS-SEM still depend on how the composites are formulated. Herman Wold proposed to use mode AModemode A to compute the scores for constructs with reflective indicators. However, Yuan and Deng recently showed that composites under mode BModemode B enjoy better psychometric properties. The authors thus proposed a structured transformation from mode AModemode A to mode BModemode B, denoted as mode $$\mathrm{B_A}$$ . This chapter further studies properties of the three modes of PLS-SEM. Analytical and numerical results show that (1) Mode AModemode A does not possess any solid statistical or psychometric properties, (2) Mode BModemode B possesses good theoretical properties but is over sensitive to sampling errorsSampling errors, and (3) Mode $$\mathrm{B_A}$$ possesses good theoretical properties as well as numerical stability. The performances of the three modes are also illustrated with two real data examples.