Using confirmatory composite analysis to assess emergent variables in business research

Henseler, J., & Schuberth, F. (2020). Using confirmatory composite analysis to assess emergent variables in business research. Journal of Business Research, 120, 147-156. https://doi.org/10.1016/j.jbusres.2020.07.026Confirmatory composite analysis (CCA) was invented by Jörg Henseler and Theo K. Dijkstra in 2014 and elaborated by Schuberth et al. (2018b) as an innovative set of procedures for specifying and assessing composite models. Composite models consist of two or more interrelated constructs, all of which emerge as linear combinations of extant variables, hence the term ‘emergent variables’. In a recent JBR paper, Hair et al. (2020) mistook CCA for the measurement model evaluation step of partial least squares structural equation modeling. In order to clear up potential confusion among JBR readers, the paper at hand explains CCA as it was originally developed, including its key steps: model specification, identification, estimation, and assessment. Moreover, it illustrates the use of CCA by means of an empirical study on business value of information technology. A final discussion aims to help analysts in business research to decide which type of covariance structure analysis to use.publishersversionpublishe

Partial Least Squares is an Estimator for Structural Equation Models: A Comment on Evermann and Rönkkö (2021)

In 2012 and 2013, several critical publications questioned many alleged PLS properties. As a consequence, PLS benefited from a boost of developments. It is, therefore, a good time to review these developments. Evermann and Rönkkö (2023) devote their paper to this task and formulate guidelines in the form of 14 recommendations. Yet, while they identified the major developments, they overlook a fundamental change, maybe because it is so subtle: the view on PLS. As mentioned by Evermann and Rönkkö (2023, p. 1), “[PLS] is a statistical method used to estimate linear structural equation models” and consequently should not be regarded as a standalone SEM technique following its own assessment criteria. Against this background, we explain which models can be estimated by PLS and PLSc. Moreover, we present the Henseler-Ogasawara specification to estimate composite models by common SEM estimators. Additionally, we review Evermann and Rönkkö’s (2023) 14 recommendations one by one and suggest updates and improvements where necessary. Further, we address their comments about the latest advancement in composite models and show that PLS is a viable estimator for confirmatory composite analysis. Finally, we conclude that there is little value in distinguishing between covariance-based and variance-based SEM—there is only SEM

Which equations? An inquiry into the equations in partial least squares structural equation modeling

Schuberth, F., Müller, T., & Henseler, J. (2021). Which equations? An inquiry into the equations in partial least squares structural equation modeling. In I. Kemény, & Z. Kun (Eds.), New perspectives in serving customers, patients, and organizations: A Festschrift for Judit Simon (pp. 96-115). Corvinus University of Budapest.Over the last decade, partial least squares structural equation modeling (PLSSEM) has undergone various enhancements. However, the model equations underlying PLS-SEM have hardly been discussed in the PLS-SEM literature. Consequently, applied researchers are left unaware of the assumptions attached to these equations and risk unintentionally misspecifying their models. This chapter addresses this issue and reveals the model equations including the implicit assumptions underlying PLS-SEM.publishersversionpublishe

A refinement of the Henseler–Ogasawara specification

Yu, X., Schuberth, F., & Henseler, J. (2023). Specifying composites in structural equation modeling: A refinement of the Henseler–Ogasawara specification. Statistical Analysis and Data Mining. https://doi.org/10.1002/sam.11608. ---Funding Information: FCT Fundação para a Ciência e a Tecnologia (UIDB/04152/2020)Structural equation modeling (SEM) plays an important role in business and social science and so do composites, that is, linear combinations of variables. However, existing approaches to integrate composites into structural equation models still have limitations. A major leap forward has been the Henseler–Ogasawara (H–O) specification, which for the first time allows for seamlessly integrating composites into structural equation models. In doing so, it relies on emergent variables, that is, the composite of interest, and one or more orthogonal excrescent variables, that is, composites that have no surplus meaning but just span the remaining space of the emergent variable's components. Although the H–O specification enables researchers to flexibly model composites in SEM, it comes along with several practical problems: (i) The H–O specification is difficult to visualize graphically; (ii) its complexity could create difficulties for analysts, and (iii) at times SEM software packages seem to encounter convergence issues with it. In this paper, we present a refinement of the original H–O specification that addresses these three problems. In this new specification, only two components load on each excrescent variable, whereas the excrescent variables are allowed to covary among themselves. This results in a simpler graphical visualization. Additionally, researchers facing convergence issues of the original H–O specification are provided with an alternative specification. Finally, we illustrate the new specification's application by means of an empirical example and provide guidance on how (standardized) weights including their standard errors can be calculated in the R package lavaan. The corresponding Mplus model syntax is provided in the Supplementary Material.publishersversionotherepub_ahead_of_prin

a confirmatory approach to study tourism technology and tourist behavior

Purpose: As technology in tourism and hospitality (TTH) develops technical artifacts according to visitors’ demands, it must deal with both behavioral and design constructs in the context of structural equation modeling (SEM). While behavioral constructs are typically modeled as common factors, the study at hand introduces the composite into TTH to model artifacts. To deal with both kinds of constructs, this paper aims to exploit partial least squares path modeling (PLS-PM) as a confirmatory approach to estimate models containing common factors and composites. Design/methodology/approach: The study at hand presents PLS-PM in its current form, i.e. as a full-fledged approach for confirmatory purposes. By introducing the composite to model artifacts, TTH scholars can use PLS-PM to answer research questions of the type “Is artifact xyz useful?”, contributing to a further understanding of TTH. To demonstrate the composite model, an empirical example is used. Findings: PLS-PM is a promising approach when the model contains both common factors and composites. By applying the test for overall model fit, empirical evidence can be obtained for latent variables and artifacts. In doing so, researchers can statistically test whether a developed artifact is useful. Originality/value: To the best of the authors’ knowledge, this is the first study to discuss the practical application of composite and common factor models in TTH research. Besides introducing the composite to model artifacts, the study at hand also guides scholars in the assessment of PLS-PM results.publishersversionpublishe

HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling

Roemer, E., Schuberth, F., & Henseler, J. (2021). HTMT2– an improved criterion for assessing discriminant validity in structural equation modeling. Industrial Management and Data Systems, 121(12), 2637-2650. https://doi.org/10.1108/IMDS-02-2021-0082Purpose: One popular method to assess discriminant validity in structural equation modeling is the heterotrait-monotrait ratio of correlations (HTMT). However, the HTMT assumes tau-equivalent measurement models, which are unlikely to hold for most empirical studies. To relax this assumption, the authors modify the original HTMT and introduce a new consistent measure for congeneric measurement models: the HTMT2. Design/methodology/approach: The HTMT2 is designed in analogy to the HTMT but relies on the geometric mean instead of the arithmetic mean. A Monte Carlo simulation compares the performance of the HTMT and the HTMT2. In the simulation, several design factors are varied such as loading patterns, sample sizes and inter-construct correlations in order to compare the estimation bias of the two criteria. Findings: The HTMT2 provides less biased estimations of the correlations among the latent variables compared to the HTMT, in particular if indicators loading patterns are heterogeneous. Consequently, the HTMT2 should be preferred over the HTMT to assess discriminant validity in case of congeneric measurement models. Research limitations/implications: However, the HTMT2 can only be determined if all correlations between involved observable variables are positive. Originality/value: This paper introduces the HTMT2 as an improved version of the traditional HTMT. Compared to other approaches assessing discriminant validity, the HTMT2 provides two advantages: (1) the ease of its computation, since HTMT2 is only based on the indicator correlations, and (2) the relaxed assumption of tau-equivalence. The authors highly recommend the HTMT2 criterion over the traditional HTMT for assessing discriminant validity in empirical studies.publishersversionpublishe

Confirmatory composite analysis in human development research

Schamberger, T., Schuberth, F., & Henseler, J. (2022). Confirmatory composite analysis in human development research. International Journal of Behavioral Development. https://doi.org/10.1177/01650254221117506 ----------- The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: J.H. gratefully acknowledges financial support from FCT Fundação para a Ciência e a Tecnologia (Portugal), and national funding through research grant Information Management Research Center—MagIC/NOVA IMS (UIDB/04152/2020).Research in human development often relies on composites, that is, composed variables such as indices. Their composite nature renders these variables inaccessible to conventional factor-centric psychometric validation techniques such as confirmatory factor analysis (CFA). In the context of human development research, there is currently no appropriate technique available for assessing composites with the same degree of rigor comparable to that known from CFA. As a remedy, this article presents confirmatory composite analysis (CCA), a statistical approach suitable to assess composites. CCA is a special type of structural equation modeling that consists of model specification, model identification, model estimation, and model assessment. This article explains CCA and its steps. In addition, it illustrates CCA’s use by means of an illustrative example.publishersversionepub_ahead_of_prin

A clarification of confirmatory composite analysis (CCA)

Hubona, G. S., Schuberth, F., & Henseler, J. (2021). A clarification of confirmatory composite analysis (CCA). International Journal Of Information Management, 61, 1-8. [102399]. https://doi.org/10.1016/j.ijinfomgt.2021.102399Confirmatory composite analysis (CCA) is a structural equation modeling (SEM) technique that specifies and assesses composite models. In a composite model, the construct emerges as a linear combination of observed variables. CCA was invented by Jörg Henseler and Theo K. Dijkstra in 2014, was subsequently fully elaborated by Schuberth et al. (2018), and was then introduced into business research by Henseler and Schuberth (2020b). Inspired by Hair et al. (2020), a recent article in the International Journal of Information Management (Motamarri et al., 2020) used the same term ‘confirmatory composite analysis’ as a technique for confirming measurement quality in partial least squares structural equation modeling (PLS-SEM) specifically. However, the original CCA (Henseler et al., 2014; Schuberth et al., 2018) and the Hair et al. (2020) technique are very different methods, used for entirely different purposes and objectives. So as to not confuse researchers, we advocate that the later-published Hair et al. (2020) method of confirming measurement quality in PLS-SEM be termed ‘method of confirming measurement quality’ (MCMQ) or ‘partial least squares confirmatory composite analysis’ (PLS-CCA). We write this research note to clarify the differences between CCA and PLS-CCA.publishersversionpublishe

the case of composites of composites

Schuberth, F., Rademaker, M. E., & Henseler, J. (2020). Estimating and assessing second-order constructs using PLS-PM: the case of composites of composites. Industrial Management and Data Systems, 120(12), 2211-2241. https://doi.org/10.1108/IMDS-12-2019-0642Purpose: The purpose of this study is threefold: (1) to propose partial least squares path modeling (PLS-PM) as a way to estimate models containing composites of composites and to compare the performance of the PLS-PM approaches in this context, (2) to provide and evaluate two testing procedures to assess the overall fit of such models and (3) to introduce user-friendly step-by-step guidelines. Design/methodology/approach: A simulation is conducted to examine the PLS-PM approaches and the performance of the two proposed testing procedures. Findings: The simulation results show that the two-stage approach, its combination with the repeated indicators approach and the extended repeated indicators approach perform similarly. However, only the former is Fisher consistent. Moreover, the simulation shows that guidelines neglecting model fit assessment miss an important opportunity to detect misspecified models. Finally, the results show that both testing procedures based on the two-stage approach allow for assessment of the model fit. Practical implications: Analysts who estimate and assess models containing composites of composites should use the authors’ guidelines, since the majority of existing guidelines neglect model fit assessment and thus omit a crucial step of structural equation modeling. Originality/value: This study contributes to the understanding of the discussed approaches. Moreover, it highlights the importance of overall model fit assessment and provides insights about testing the fit of models containing composites of composites. Based on these findings, step-by-step guidelines are introduced to estimate and assess models containing composites of composites.authorsversionpublishe