A Critical Assessment for Sport Management Research: Comparing PLS-SEM and CB-SEM Techniques for Moderation Analysis Using Formative Measures

Abstract

Historically, researchers in the sport management area have used covariance based structural equation modeling (CB-SEM) when testing complex models. Recently, researchers have been using partial least squares path modeling (often called PLS-SEM) more frequently. The purpose of this paper was to advise sport management researchers about what approach to use by comparing PLS-SEM versus CB-SEM analytical techniques on the two different types of models: a formative (composite indicator) multigroup model and, a formative (composite indicator) continuous interaction model. We collected data from individuals (N = 1155) in the New England area (USA). After testing a base model, a multigroup model, and a continuous interaction model, we feel that PLS-SEM is the better choice for sport management researchers when testing formative models that use a composite variable. Our research shows when and why each technique works, in addition to showing that PLS-SEM moderation and multigroup models with formative items can work in the R statistical software.

Keywords:

• CB-SEM
• PLS-SEM
• formative multigroup model
• formative continuous interaction model
• R statistical software

Disclosure Statement

No potential conflict of interest has to be reported.

Notes

1 Typically researchers refer to constructs or latent variables instead of common factors or composites. Rigdon et al. (2017) argue that latent variables are features of theoretical or conceptual models and not statistical models. This contradicts most CB-SEM textbooks and articles that predominantly use “latent” variable nomenclature to represent common factor variables (e.g. Bollen & Bauldry, 2011; Hair et al., 2017; Hwang, Sarstedt, Cheah, & Ringle, 2020; Nicewander, 2020) and we will continue to do so.

2 We are using the term composite (or formative) indicator rather than the term causal indicator, which many researchers use to describe this type of indicator. Bollen and Bauldry (2011) made a distinction between different types of indicators, noting that there are effect (reflective) indicators and three types of formative indicators: causal, composite, and covariates. Causal indicators are those indicators that cause the latent variable (e.g. job change, divorce, and moving, may all cause life stress - the latent variable). Composite indicators are the components of the composite variable and are a linear combination (e.g. product, price, place, and promotion may all be composite (formative) indicators of the marketing mix (latent variable)). Composite models assume a “definitorial rather than a causal relationship between indicators and the emergent (latent) variable (Benitez et al., 2020, p. 3).These emergent variables can also be called “artifacts”, which are “human made creations that are shaped and built by their ingredients to serve a certain goal” Benitez et al., 2020, p.1).Covariates are not measures of the latent variable per se, but their inclusion as an indicator may be necessitated to “avoid potential omitted variable bias” (Bollen & Bauldry, 2011, p. 266).

3 However, Mathews et al. (2018), argue that continuous moderators cannot be used in CB-SEM, and Hair, Sarstedt, & Ringle (2019) argue that the constraints required to make the models function in CB-SEM “contradict theoretical considerations” (p. 568).

4 Furthermore, if one of the behavioral intention latent constructs were removed or if the DVs were solely manifest variables (e.g. attendance intentions or TV watching intentions), the CB-SEM model became unidentified (see authors for details). However, both of the latter models still work in PLS-SEM because PLS-SEM does not check for identification (which means that if the model is non-identified, the estimates cannot be trusted; Henseler et al., 2016). In addition, if, as per MacCallum and Browne (1993), the composite variables are removed, and the formative items directly predict either a latent dependent variable (e.g. Future Media Behavior) or a manifest DV, the model will also work in CB-SEM.

5 We came across several other suggestions on how to code composite (formative) item models using Mplus within the Mplus discussion boards and literature. We tried several of the variations, but none of those codings created a model that would terminate within the requisite iterations (10,000) or a model that was identified (see authors for details).

6 Klesel et al. (2019), however, claim that previous approaches of multigroup analysis in PLS-SEM “have serious drawbacks” (p. 465) because they do not compare the whole model, rely on distributional assumptions, and may have high family-wise error rate. They suggest using their proposed geodesic distance technique to alleviate the noted concerns of prior techniques. In our situation though, we were not interested in comparing the whole model and using the geodesic distance technique provides only a single test rather than the different invariance tests we applied, specifically because we were interested in the different invariances. Second, we had no violations of distributional assumptions, so that was not an issue. Third, family-wise error rate was also not much of an issue since we only had 4 groups.

7 As an aside, as we noted, the base model worked in both CB-SEM and PLS-SEM. We compared the results of the variance explained by each of the formative items on both the future consumer behavior (FCB) and on the future media behavior (FMB) latent variables using each technique. The variance explained in each DV was extremely close using the different techniques. We also compared the results to a multivariate regression with the formative items as IVs and the DVs being the mean score of the three reflective items for each DV (i.e., FCB & FMB). The variance explained using the multiple regression was very similar to the other two techniques. This is not really surprising as PLS is a regression technique with the addition of path analysis capabilities and when CB-SEM is used to test models like this, it is a combination of regression, path analysis, and factor analysis.

Additional information

Notes on contributors

Galen T. Trail

Galen T. Trail (Ph.D., The Ohio State University, US) is a Professor Emeritus in the Marketing Department in the Albers School of Business & Economics at Seattle University. His main area of research focuses on consumer behavior in sport, and he has published over 80 books, book chapters and articles and been cited almost 10,000 times. In the last several years though, he has applied his expertise in sport consumer behavior/marketing to a new endeavor: Assisting sport organizations to help their fans, spectators, or participants improve environmentally sustainable behaviors both at the event and at home. This focus on marketing sustainability through sport has led to multiple research projects over the last several years working with sport organizations to improve their sustainability marketing and communications.

Yu Kyoum Kim

Yukyoum Kim is a Professor of Physical Education at the Seoul National University. He earned his Ph.D. from the University of Florida in 2008. The same year, he started as an assistant professor at the Florida State University, where he became a tenured professor in 2013. Dr. Kim has worked on questions of psychological health and wellbeing through bodily experience, including vicarious achievement, gratitude, relationship quality, constraints and motivation. He has published his work in such journals as Journal of Sport Management, Sport Management Review, Sport Marketing Quarterly, and European Sport Management Quarterly.

Priscila Alfaro-Barrantes

Priscila Alfaro-Barrantes (Ph.D., The Florida State University, US) is a professor a Professor of Sport Management in the College of Business at Nichols College, Dudley, Massachusetts. Her research interests include social corporate responsibility, experiential learning, and talent acquisition. She has presented at the North American Society for Sport Management, Sport Marketing Association Conference, among others.