How Are We Testing Interactions in Latent Variable Models? Surging Forward or Fighting Shy?

Abstract

Latent variable models and interaction effects have both been common in the organizational sciences for some time. Methods for incorporating interactions into latent variable models have existed since at least Kenny and Judd, and a great many articles and books have developed these methods further. In the present article, we present an empirical review of the methods that organizational science investigators use to test their interaction hypotheses. We show that it is very common for investigators to use fully latent methods to test additive portions of their models, but to abandon such methods when testing the multiplicative portions of their models. By contrast, investigators whose models do not contain interactions tend to stick with fully latent methods throughout. As there is little rational basis for this pattern, it is likely due to continued discomfort regarding the proper application of existing fully latent methods. Thus, we end by offering R code that implements some of the more sophisticated fully latent approaches, and by offering a sequence of decisions that investigators can follow in order to choose the best analytic approach.

Comparison of Composites, Dichotomous, and Latent Factor Measurement Operationalizations in Hospitality Research on Moderating Effects

“…Specifically, when researchers test relationships among reflective constructs that do not involve interactions using latent factor models and in the interaction testing step ignore the reflective measurement model of the moderator, they send an inconsistent message about the theoretical assumptions to the reader. Our call to hospitality researchers is consistent with pleas in other business areas, such as organizational behavior, where researchers equally welcome latent models as long as they do not test for interaction effects (Cortina et al, 2020). We advise hospitality researchers to branch out beyond the inherited construct operationalizations and statistical traditions and practice uniformity in selected procedures.…”

Beyond a tandem analysis of SEM and PROCESS: Use of PLS-SEM for mediation analyses!

“…Recent research has shown that correcting for measurement error is particularly critical when dealing with interaction terms—as required to specify a moderating effect in, for example, conditional process models (Li et al, 2019). The reason is that the attenuating effect of measurement error is exacerbated in the product of two error-prone measures (Cortina et al, 2020). For instance, when a predictor and moderator are uncorrelated, the reliability of the interaction term is the product of the predictor’s and moderator’s reliabilities (Aguinis et al, 2017; Busemeyer & Jones, 1983).…”

“…A common objection regarding the use of SEM for estimating conditional process models is that the estimation of interaction terms is far from trivial, and its specification is still subject to debate in the methodological literature (e.g., Cortina et al, 2001, 2020; Sardeshmukh & Vandenberg, 2017). Commenting on these issues, Hayes et al (2017) note that “it can be difficult to trust a model which involves estimating latent variable interactions because it is difficult to determine whether the resulting estimates of interactions are reasonable” (p. 80).…”

“…The use of composite-based SEM for conditional process models can address recent concerns regarding the application of latent approaches to test mediation effects but reverting to non-latent approaches (e.g., PROCESS) to test moderation effects within the same model (Cheung & Lau, 2017; Cortina et al, 2020; Sardeshmukh & Vandenberg, 2017). As Cortina et al (2020) note,Using latent variable modeling for additive portions [i.e., the main effects] and dropping them for multiplicative portions [i.e., the interaction term] is akin to putting on the parking brake in Cleveland but leaving it off in Columbus: Either you think that the break does something worthwhile or you don’t.…”

Self-efficacy, mental models and team adaptation: A first approach on football and futsal refereeing

“…The latent moderation variable was produced using the semTools package (Jorgensen et al, 2019) using match-paired approach (Marsh, Wen, & Hau, 2004) and double-mean centring for the product of the indicators (Lin, Wen, Marsh, & Lin, 2010). When testing the moderation effects of variables that are not directly observed, the measurement error should be accounted, as such, latent variable moderation should be preferred (Cortina, Markell-Goldstein, Green, & Chang, 2019;Sarstedt, Hair, Nitzl, Ringle, & Howard, 2020). The idea that measurement error can be ignored consists of what Edwards (2009) classified as one "of the seven deadly myths of testing moderation" (p. 143).…”