A Comparison of Approaches for the Analysis of Interaction Effects Between Latent Variables Using Partial Least Squares Path Modeling

Abstract

In social and business sciences, the importance of the analysis of interaction effects between manifest as well as latent variables steadily increases. Researchers using partial least squares (PLS) to analyze interaction effects between latent variables need an overview of the available approaches as well as their suitability. This article presents 4 PLS-based approaches: a product indicator approach (Chin, Marcolin, & Newsted, 2003 Chin, W. W., Marcolin, B. L. and Newsted, P. R. 2003. A partial least squares latent variable modeling approach for measuring interaction effects: Results from a Monte Carlo simulation study and an electronic-mail emotion/adoption study. Information Systems Research, 14: 189–217. [Crossref], [Web of Science ®] , [Google Scholar]), a 2-stage approach (Chin et al., 2003 Chin, W. W., Marcolin, B. L. and Newsted, P. R. 2003. A partial least squares latent variable modeling approach for measuring interaction effects: Results from a Monte Carlo simulation study and an electronic-mail emotion/adoption study. Information Systems Research, 14: 189–217. [Crossref], [Web of Science ®] , [Google Scholar]; Henseler & Fassott, in press), a hybrid approach (Wold, 1982 Wold, H. 1982. “Soft modeling: The basic design and some extensions”. In Systems under indirect observation: Causality, structure, prediction, 2 Edited by: Jöreskog, K. G. and Wold, H. 1–54. Amsterdam: North-Holland. [Google Scholar]), and an orthogonalizing approach (Little, Bovaird, & Widaman, 2006 Little, T. D., Bovaird, J. A. and Widaman, K. F. 2006. On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables. Structural Equation Modeling, 13: 497–519. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and contrasts them using data related to a technology acceptance model. By means of a more extensive Monte Carlo experiment, the different approaches are compared in terms of their point estimate accuracy, their statistical power, and their prediction accuracy. Based on the results of the experiment, the use of the orthogonalizing approach is recommendable under most circumstances. Only if the orthogonalizing approach does not find a significant interaction effect, the 2-stage approach should be additionally used for significance test, because it has a higher statistical power. For prediction accuracy, the orthogonalizing and the product indicator approach provide a significantly and substantially more accurate prediction than the other two approaches. Among these two, the orthogonalizing approach should be used in case of small sample size and few indicators per construct. If the sample size or the number of indicators per construct is medium to large, the product indicator approach should be used.