Selection of Indicators for the Interaction Term in Structural Equation Models with Interaction

Abstract

Kenny and Judd (1984, Psychological Bulletin 96: 201-210) suggested using structural equation models to model interaction effects since they allow correction for measurement error. They proposed using all possible products of the indicators of the two interacting variables as indicators for the interaction term. Jöreskog and Yang (1996, Advanced Structural Equation Modeling. Mahwah, NJ: Lawrence Erlbaum, pp. 57-88.) defended that this is not necessary; one product variable is sufficient to estimate the interaction effect. However, they did not specify which indicators should be chosen if there is more than one possibility. We prove that the optimal choice is to select the indicators with the highest reliabilities. But this is only true if certain assumptions hold. We go on to show that one can get very different results depending on the indicators chosen for the interaction term if the indicators are not congeneric which is often the case. These methodological arguments will be illustrated by a study of the purchasing or boycotting of certain products for environmental reasons.

Estimating Latent Variable Interactions with the Unconstrained Approach: A Comparison of Methods to Form Product Indicators for Large, Unequal Numbers of Items

“…However, they did not provide any guidance on how to choose the best indicators to create the product indicator. Recently, Saris, Batista-Foguet, and Coenders (2007) proved that the best indicators to form a single indicator product are the ones with the highest reliability.…”

“…Saris et al (2007) proved that for the constrained method where a single indicator is used, this single indicator should be the most reliable one. However, Saris et al's study using a single indicator with the constrained model is quite different from the multiple-indicator unconstrained model that is the focus of this study.…”

Person–place congruency in the Internet Banking context

“…However, MRA assumes that the explanatory variables are error-free (Irwin and McClelland, 2001); otherwise, the analysis results in biased estimations of the interaction effects (Saris et al, 2007). The most common methods to address this problem are SEM based techniques (Marsh et al, 2004).…”

Integration of Moderation and Mediation in a Latent Variable Framework: A Comparison of Estimation Approaches for the Second-Stage Moderated Mediation Model

“…Another limitation of the PI approach is the difficulty researchers face in choosing among multiple indicators to construct the product indicators for the latent interaction factor (Marsh et al, 2004 ). Different strategies to construct the product indicators in the same model may perform differently (e.g., Marsh et al, 2004 ; Saris et al, 2007 ; Aytürk et al, 2019 ). Researchers need to choose suitable strategies to get a reasonable result, which makes the application of the PI approach a challenge.…”