A brief review of partial least squares structural equation modeling (PLS-SEM) use in quality management studies

Purpose – Partial least squares structural equation modeling (PLS-SEM) has become an established social sciences multivariate analysis technique. Since quality management researchers also increasingly using PLS-SEM, this growing interest calls for guidance. Design/methodology/approach – Based on established guidelines for applying PLS-SEM and evaluating the results, this research reviews 107 articles applying the method and published in eight leading quality management journals. Findings – TheuseofPLS-SEMinqualitymanagementoftenonlydrawsonlimitedinformationandanalysis results. The discipline would benefit from the method ’ s more comprehensive use by following established guidelines.Specifically,theuseofpredictivemodelassessmentandmoreadvancedPLS-SEManalysesharborsthepotentialtoprovidemoredetailedfindingsandconclusionswhenapplyingthemethod. Research limitations/implications – This research provides first insights into PLS-SEM ’ s use in quality management.Futureresearchshouldidentifythekeyareasandthe corequalitymanagementmodelsthatbest support the method ’ s capabilities and researchers ’ goals. Practical implications – The results of this analysis guide researchers who use the PLS-SEM method for their quality management studies. Originality/value – This is the first article to systematically review the use of PLS-SEM in the quality management discipline.


Introduction
Partial least squares structural equation modeling (PLS-SEM; Hair et al., 2022;Lohm€ oller, 1989;Wold, 1982) has become an established social sciences multivariate analysis technique (e.g. . Since quality management researchersas we show in this articlealso increasingly use PLS-SEM, this growing interest requires guidance. Consequently, we provide a critical review of PLS-SEM's usage in 107 studies published in leading quality management journals. Our review is based on established guidelines for applying the PLS-SEM method and evaluating the results (e.g. Hair et al., 2019a;Sarstedt et al., 2020). Furthermore, we refer to PLS-SEM applications' relevant criteria and aspects considered in prior review studies (e.g. Hair et al., 2012;Ringle et al., 2020;Sarstedt et al., 2022a).
Our goal is not to provide a complete review, which previous studies have done, but a first insight into PLS-SEM's use in quality management. In addition, we offer the first suggestions for improving researchers' application practices. Consequently, our review focuses on four aspects: (1) reasons for using PLS-SEM, (2) model characteristics, (3) structural model evaluation, and (4) advanced analysis techniques. We exclude the complex topic of measurement model evaluation from this initial analysis in quality management, since our review clarifies that, at first glance, an appropriate PLS-SEM application in this discipline has comparable problems to those that review studies in other disciplines have already identified (see Table 1 in Cepeda-Carri on et al., 2022, which provides an overview of PLS-SEM review studies in different research disciplines). Consequently, quality management researchers are advised to follow the established guidelines for measurement model evaluation (e.g. Hair et al., 2019a;Legate et al., 2022;Sarstedt et al., 2021). For instance, it is important to fully apply the current and relevant criteria catalog to the evaluation and not to only highlight a few aspects when assessing PLS-SEM results.
In the following subsections, we explain how we selected articles comprising PLS-SEM quality management applications and present the results of our review of the four aspects (reasons, characteristics, structural model, and advanced techniques) on which it focuses. Our analysis reveals key findings regarding PLS-SEM's usage in quality management and the latter's potential for improving the method's application. We therefore provide guidance for the PLS-SEM method's utilization in quality management and related fields.

PLS-SEM applications in quality management
We review PLS-SEM applications in quality management by considering the eight quality management journals included in the 2021 British Association of Business Schools (ABS, field: operations and technology management): TQM journal (Emerald, 1* ABS), International Journal of Quality and Reliability Management (Emerald, 2* ABS), Total Quality Management and Business Excellence (Taylor and Francis, 2* ABS), International Journal of Productivity and Quality Management (Inderscience, 1* ABS), International Journal of Quality and Service Sciences (Emerald, 1* ABS), Journal of Quality in Maintenance Engineering (Emerald, 1* ABS), Quality and Reliability Engineering International (Wiley-Blackwell, 1* ABS), and Quality Progress (American Society for Quality Control, 1* ABS). We subsequently undertook a full-text search of Elsevier's Scopus database for articles published in the eight journals during 2021 (last update, January 20, 2022), using the search terms "PLS-SEM" and "partial least squares." The query yielded 137 articles. Once we had assessed each of these articles to determine whether they applied PLS-SEM and contained the information required for the study, we excluded 30 articles from the review. This exclusion was due to articles not applying PLS-SEM (i.e. only mentioning PLS-SEM or using PLS regression, n 5 12; not reporting sufficient information for an evaluation, n 5 11; discussing the methodology, n 5 5; and only using PLS-SEM for scale development, n 5 2). A total of 107 articles were ultimately selected and reviewed. Six of them included more than one model, providing a total of 124 path models for our review. One of these 6 articles studied the relationship between the predictive value and the frequency of utilization of 12 maintenance measures and, for this purpose, estimated 12 different models (Gomes et al., 2021). The other 5 articles included multiple models which differed with regard to some variables. For example, Ajami et al. (2018)

Reasons for using PLS-SEM
Our review reveals that 17 articles do not report reasons for using PLS-SEM. The remaining 90 articles provide one or more reasons to motivate PLS-SEM's application (Table 1). The two most frequently mentioned reasons are the small sample size (50 studies) and the nonnormal   . In fact, PLS-SEM's causal-predictive nature makes it a useful method when a study's purpose is to balance explanation and prediction, therefore "perfectly fitting today's research environment, which is not only concerned with testing hypothesized models but also with deriving managerial recommendations that are predictive by nature" (Becker et al., 2022a). The results of our review indicate that quality management researchers focus strongly on data characteristic-related arguments. Other, frequently reported reasons are the high model complexity (23 studies), theory development and exploratory research (20 studies), and the predictive study focus (18 studies). All these reasons are valid arguments for choosing PLS-SEM. However, PLS-SEM researchers should specifically emphasize the research goals of their studies (Sarstedt et al., 2022b).

Model characteristics
As explained above, model complexity is a possible reason for selecting PLS-SEM. In fact, PLS-SEM can successfully handle complex models, such as those that include very many constructs and indicators, reflective and formative measurement models, mediation and moderation effects, higher-order constructs, and nonlinear relationships.
Our analysis of the 124 path models shows an average of 5.72 latent variables and an average of 7.60 path relationships (Table 2). These values are lower than those reported in fields such as marketing , in which researchers started widely adopting PLS-SEM long before those in the quality management field did so. In addition, 119 of the 124 models only comprise reflectively measured constructs. A remarkable share of the reviewed models (43.54%) includes mediation effects. One or more higher-order constructs are present in 32 articles employing Type I (reflective-reflective; 17 studies), Type II (reflective-formative; 9 studies) or both Type I and Type II (2 studies) second-order constructs. Four studies do not provide information about the type of higher-order construct. Overall, most of the studies do not present plausibly comprehensible procedures for higher-order constructs' specification, estimation, and validation (for example, see Sarstedt et al., 2019). For instance, only 10 of the 32 studies describe the approach for specifying and estimating higher-order constructs, revealing that the two-stage approach (7 studies) is more frequently applied than the repeated indicators one (3 studies). In only 3 studies are the higher-order constructs evaluated in a meaningful way (for example, see Becker et al., 2022a;Sarstedt et al., 2019). Moreover, in 13 studies, the assessment procedures are incompletely applied (e.g. they do not mention the discriminant validity evaluation between the lower-order components, nor are the formative higher-order constructs subjected to a redundancy analysis). In 13 studies, the higher-order constructs are not evaluated at all, and, in the remaining 3 studies, the evaluation criteria are misapplied (e.g. the relationships between the lower-order components and the higher-order components are considered structural paths).

Structural model evaluation
The evaluation of the structural model comprises assessing the model's explanatory and predictive power and the path coefficients' significance and relevance. The results of our analysis (Table 3) highlight that almost all models (123 and 122 models, respectively) report the path coefficients' values and significance. In 119 models, the path coefficients' significance is tested by means of the bootstrapping routine. Information about the number of bootstrap samples is only provided in 64 models (51.61%). Specifically, 5,000 bootstrap samples are used in the evaluation of 42 models, from 1,000 to 2,000 samples in the analysis of 6 models, and 500 or fewer samples in the assessment of 16 models. None of the reviewed PLS-SEM applications is therefore consistent with the more recent literature, which recommends drawing on at least 10,000 bootstrap samples (Becker et al., 2022a;Streukens and Leroi-Werelds, 2016). The bootstrapping confidence intervals, as well as the standard errors, t values, and/or p values, are reported in 23 models. However, two models only provide the bootstrapping confidence intervals in respect of the indirect effects, but not the direct effects. More recent guidance on PLS-SEM applications recommends using bootstrap confidence intervals routinely when testing inference (e.g. Sarstedt et al., 2022b). In addition, the f 2 effect size is evaluated in 37 models.
Predictive model assessment is a core motivation for selecting PLS-SEM (Hair et al., 2019a). In this regard, the distinction between a model's explanatory and predictive power was a central argument in PLS-SEM's recent developments (Sarstedt et al., 2022b). The explanatory power is assessed in 114 models by means of the value of the coefficient of A brief review of PLS-SEM use determination (R 2 ). In some cases, the model fit measures are also reported, although they should be used cautiously in PLS-SEM (Hair et al., 2019b). Specifically, the goodness-of-fit index (GoF; 23 models) of Tenenhaus et al. (2005), although criticized (Henseler and Sarstedt, 2013), and the standardized root mean square residual (SRMR; 6 models) are the most used model fit measures. In terms of their predictive relevance, a significant proportion of the models are evaluated by means of the Q 2 (58 models) and the q 2 (14 models), which are based on the blindfolding routine. However, recent research has advised against the use of Q 2 and q 2 resulting from Blindfolding to assess a model's predictive power with PLS-SEM and has recommended applying the PLS predict procedure (Shmueli et al., 2016. Most certainly because of its novelty, none of the reviewed studies applied PLS predict . In addition, no study compares competing models' predictive power by using novel procedures such as the crossvalidated predictive ability test (CVPAT; Liengaard et al., 2021;Sharma et al., 2022). We expect the evaluation of models' predictive power and predictive model comparison to become an established routine in quality management studies applying PLS-SEM within the near future.

Advanced analysis techniques
Finally, the articles' review examines the application of advanced analysis techniques. While PLS-SEM research is continuously evolving and developing new advanced analysis techniques (e.g. Hair, 2021; and robustness checks (e.g. Richter et al., 2020;Sarstedt et al., 2020), our review reveals that quality management researchers scarcely apply them. For example, none of the articles uses latent class analyses (e.g. FIMIX-PLS, PLS-POS) to evaluate unobserved heterogeneity (Becker et al., 2013;Hahn et al., 2002) or confirmatory tetrad analysis (CTA-PLS) to support the choice of reflective or formative measurement model specification (Gudergan et al., 2008). Overall, of the 107 articles, only one includes PLS-SEM's importance-performance analysis (IPMA; Ringle and Sarstedt, 2016). Specifically, Raharjo et al. (2016) apply IPMA to assess predecessor constructs' performance and importance in shaping patient and care  Table 3. Structural model evaluation provider satisfaction, and extend their analysis on the indicator level. While multigroup analysis is reported in 9 studies, the MICOM procedure is only used in 3 of them to assess measurement invariance (Henseler et al., 2016). This finding raises concerns, because measurement invariance is a prerequisite for multigroup analysis (e.g. Hair et al., 2022). Finally, 2 articles mention endogeneity assessment briefly, but the authors do not provide the results and/or any other information about the applied procedure.

Conclusions and future research
The PLS-SEM method is increasingly used in quality management and has established itself as a standard method with growing relevance. This method has a special importance in the discipline, especially for models with success factors (Aquilani et al., 2017;Carmona-M arquez et al., 2016) or for investigating the sources of a competitive advantage (El Shenawy et al., 2007;Sciarelli et al., 2020). Simultaneously, however, PLS-SEM's use in quality management reveals various areas of improvement, which we specifically uncovered in the following areas: (1) reasons for using PLS-SEM, (2) the model characteristics, (3) structural model evaluation, and (4) advanced analysis techniques. Authors and reviewers should follow the established guidelines more closely (e.g. Hair et al., 2019a;Sarstedt et al., 2022a) to improve the application of the method in the future. In addition, it is noticeable that in the quality management area, methodological PLS-SEM innovations are adopted very late. This specifically applies to robustness checks , which include, for example, nonlinear effects, endogeneity, and unobserved heterogeneity but also the confirmatory tetrad analysis (Gudergan et al., 2008). Moreover, extended PLS-SEM analyses, such as the IPMA , have been established for some time, but are hardly taken into account. In more recent methodological developments, prediction-based model evaluation (Sharma et al., 2022;Shmueli et al., 2019), prediction-based model comparison and selection (Liengaard et al., 2021;Sharma et al., 2019), the detection and treatment of endogeneity issues by means of Gaussian copulas (Becker et al., 2022b;Eckert and Hohberger, 2022;Hult et al., 2018;Park and Gupta, 2012), the necessary condition analysis (Dul, 2016(Dul, , 2020Richter et al., 2020) and the conditional mediation analysis (Cheah et al., 2021) have, however, received particular attention. Finally, researchers should employ appropriate methods to assess observed heterogeneity via moderator (e.g. Becker et al., 2022a;Becker et al., 2018) and multigroup analyses (e.g. Chin and Dibbern, 2010;, as well as unobserved heterogeneity (e.g. Sarstedt et al., 2017;Schlittgen et al., 2016) to ensure their results' validity. The methodological extensions are also of great interest for quality management research and current studies should also adopt them in a timely manner.