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The aim of this special issue of Industrial Management & Data Systems is to introduce advances in methods and metrics to a wider audience, in an effort to broaden the understanding of business and information systems applications. This special issue embraces both the methodological side of PLS-SEM and empirical research using advanced techniques.

This special issue particularly focuses on complex research that requires advanced analytical methods; confirmatory tetrad analysis to empirically assess the mode of measurement; new approaches for testing discriminant validity; mediation and moderation; prediction-oriented segmentation analysis to identify and treat unobserved heterogeneity; prediction-oriented model selection to choose between models of varying predictive utility and invariance testing by means of the measurement invariance of composite models approach. We also emphasize that while many of the previously applied metrics are still relevant, there is both room and need for newer metrics and assessment techniques. In particular, we can take advantage of recent advances in model comparison criteria, endogeneity assessment, latent class analyses and PLS-based prediction.

The advancement and assimilation of PLS-SEM methods would not be successful without the efforts and contributions from the renowned scholars in this field that include, but are not limited to, Joseph F. Hair Jr, Wynne Chin, Christian M. Ringle, Marko Sarstedt, Jörg Henseler, Galit Shmueli, Jose Luis Roldan, Gabriel Cepeda, T. Ramayah and Alain Y.-L. Chong.

The articles in this special issue of Industrial Management & Data Systems either methodologically advance existing estimation and assessment techniques in PLS-SEM or empirically demonstrate the application of state-of-the-art methodological advances. By including both methodological and empirical articles, we hope to give readers a stronger understanding of the ways in which they can broaden their understanding of phenomena in business and information systems fields.

Chin et al. (2021) aim to demystify the role of causal-predictive modeling in using PLS-SEM for Information Systems (IS) research to help researchers select the appropriate model with both explanatory and predictive power. To this end, Chin et al. (2021) first conduct a systematic review of empirical studies in IMDS and MISQ that employed casual prediction criteria in PLS-SEM. Their investigation reveals that there has been extensive reliance on criteria which were developed for assessing the explanatory power of path models (e.g. R2). However, rarely studies have applied PLSpredict, CVPAT and predictive model selection criteria for assessing predictive power. To promote the assimilation of new and suitable criteria that can balance the goals of explanation and prediction in PLS-SEM, Chin et al. (2021) provide detailed explanation on the procedures and interpretation of each casual prediction criteria available in PLS-SEM (i.e. criteria for in-sample prediction, out-of-sample prediction, model selection and fit measures). Chin et al. (2021) also provide an illustration on how to use PLS-SEM casual prediction with the empirical data from Zhang et al. (2018). A comparison of the performance of different quality criteria showed that traditional PLS-SEM criteria such as GoF, Tenenhaus, R2 and Q2 are not adequate in determining the appropriate casual-predictive model because these metrics display a pronounced preference for complex models. Overly complex models can lead to overfitting of models, which yields poor predictability and low out-of-sample generalizability. On the other hand, PLSpredict, CVPAT and other model selection criteria (i.e. BIC, BIC weight, GM, GM weight, HQ and HQC) consider both in-sample and out-of-sample predictions, and are found to outperform the aforementioned traditional metrics. Chin et al. (2021) provide a significant contribution to the development of PLS-SEM methodology by substantiating the use of PLSpredict, CVPAT and model selection criteria in casual-predictive modeling.

Schuberth et al. (2021) focus on the second-order construct in PLS-SEM modeling which is a prevailing way to operationalize complex theoretical concepts in information systems research. Schuberth et al. (2021) differentiate four types of second-order constructs – common factors of common factors, common factors of composites, composites of common factors and composites of composites. Among these four types of constructs, composites of composites, which can be used to operationalize concepts that consist of other composed concepts, has been employed the most to model second-order constructs in IS research. However, despite its practical importance and relevance, the evaluation of composites of composites remains underexplored in the structural equational modeling (SEM) literature. Motivated by this research gap, Schuberth et al. (2021) aim to: (1) show how to estimate composites of composites in PLS-SEM by comparing the performance of different PLS-SEM approaches; (2) propose and evaluate two procedures to assess the overall model fit of models containing composites of composites and (3) provide a user-friendly step-by-step guideline demonstrating how to estimate such models. To this end, Schuberth et al. (2021) first review the existing approaches to estimate models containing composites: repeated indicators approach, the two-stage approach, the hybrid approach and modified versions of these approaches. Next, Schuberth et al. (2021) introduce two strategies to assess the overall fit of such models: (1) following a two-step testing procedure and (2) assessing the complete postulated model all at once. A Monte Carlo simulation is of the population models is then used to compare the efficacy of the two proposed model-fit assessment strategies and the aforementioned model evaluation approaches. The simulation results show that for the two-stage approach, although the combination with the repeated indicators approach and the extended repeated indicators approach perform similarly, only the former combination is Fisher consistent. The results further show that recently proposed guidelines that ignore overall model fit assessment could fail to detect misspecified models. In addition, it is shown by the results that both testing procedures proposed by Schuberth et al. (2021) allow for assessment of model fit. These findings make a significant contribution to the understanding of the approaches to evaluation models containing composites of composites. Particularly, Schuberth et al. (2021) highlight the importance of overall model fit assessment and provide important insights on the procedures to test the overall fit of such models. In another important practical contribution, Schuberth et al. (2021) provide a detailed guideline on how to estimate and assess models containing composites of composites with the two-stage estimation approach and the two-step testing procedure.

Richter et al. (2021) propose a method to combine PLS-SEM with necessary condition analysis (NCA) to enable the exploration and validation of hypotheses which follow a sufficiency logic and a necessity logic. While PLS-SEM is the appropriate method to identify the relationship defined by a sufficiency logic, NCA is useful to identify the conditions specified by a necessity logic. Richter et al. (2021) thus introduce a method to complement PLS-SEM with NCA such that hypotheses following sufficiency and necessity logics could be explored and validated at the same time. Richter et al. (2021) discuss the guidelines on how to combine PLS-SEM and NCA. The guidelines provide details on how to specify the research objective and background, prepare and evaluate data, implement data analysis, evaluate measurement and structural model, and interpret results. An illustration example is provided with a technology acceptance dataset. This novel approach provides IS researchers a power tool to address the untested necessity of theoretical statements. The combination of both sufficiency and necessity logics will empower researchers to more precisely test hypotheses and statements.

The special issue also includes articles applying advanced PLS methods in various empirical contexts. Martínez-Caro et al. (2021) study how IT assimilation affects performance in the business-to-business (B2B) context, and aim to resolve the debate in the current literature on the direct relationship between IT and firm performance. Drawing on the organization capability view, a complex path model has been developed which proposes that the relationship between IT assimilation and organizational performance is mediated by absorptive capacity (both realized and potential) and organizational agility. The results of using PLS-SEM to analyze data from 110 Spanish companies showed that IT assimilation positively affected organizational agility, which in turn affected organizational performance. The relationship between IT assimilation and organizational agility was mediated by potential absorptive capacity but not by realized absorptive capacity. The authors also used PLSpredict to ascertain that the model showed high predictive power in terms of predicting firm performance. This study not only contributes to the literature on understanding how IT directly affects performance through building organizational agility, it also demonstrates how to employ PLSpredict to analyze the predictive power of a research model where there are multiple mediation relationships.

In another firm level study in this special issue, Roldan et al. (2021) focus on total quality management (TQM) and investigate how the soft and hard management factors specified in the EFQM Excellence model affect different dimensions of organizational results (i.e. consumer, people, society and key business results). Based on a sample of 225 Spanish organizations that enforced the application of EFQM Excellence Recognition Systems, Roldan et al. (2021) conducted a PLS-SEM analysis. The results of the structural model showed significant positive relationship between soft and hard factors, and confirmed significant positive impacts of these factors on the four dimensions of organizational results. The following mediation analysis (Nitzl et al., 2016) showed a complementary partial mediation of hard factors on the impacts of soft factors on customer, people and key business results of organizations. A full mediation effect of hard factors was found on the relationship between soft factors and society results. Roldan et al. (2021) not only contribute to the literature by considering the multidimensional nature of TQM, it further provides an illustration on how to conduce mediation analysis using advanced PLS-SEM methods.

Mutum et al. (2021) investigate the factors affecting the adoption of smartwatches. Based on the literature of technology resistance, this article differentiates between users with low and high levels of status quo satisfaction (i.e. passive innovation resistance) and compares these two groups in terms of the effects of relative advantage, ease of use, observability, trialability, compatibility and social influence on the attitude and adoption intention toward smartwatches. Following the MICOM procedure (Henseler et al., 2015), a PLS variance-based analysis was conducted to perform a multigroup analysis on a sample of 308 nonadopters. The results revealed that there were significant differences between the high and low status quo satisfaction users. It was found that, for low status quo satisfaction users, the paths from perceived ease of use and trialability to attitude, and the path from attitude to adoption intention, were stronger. For high status quo satisfaction users, the effect of social influence on attitude was stronger than the low status quo satisfaction group. Mutum et al. (2021) contribute empirically to the literature by considering smartwatch adoption from positive and inhibitory perspectives. Methodologically, Mutum et al. (2021) provide a demonstration on applying advanced PLS-SEM analysis techniques such as PLSpredict (Shmueli et al., 2016) and MICOM (Henseler et al., 2015) for testing multigroup differences.

Carranza Vallejo et al. (2021) provide another demonstration on multigroup analysis with advanced PLS-SEM methods by studying the differences in fast-food restaurant consumers in terms of mobile coupon usage. Drawn on the technology acceptance model (Davis et al., 1989), this study investigates the factors affecting users' behaviors toward mobile coupon, and compare the differences between expert and novice users. Based on a sample data from 619 consumers, Carranza Vallejo et al. (2021) conducted permutation test and MGA (Henseler et al., 2016) to analyze group differences. The results showed a significant difference between expert and novice users in terms of the relationship between perceived ease of use and perceived usefulness. However, no significant differences were found for other proposed relationships among attitude, coupon proneness, intention to use coupon and usage of coupon between expert and novice users. This study contributes to the literature of technology acceptance with a special focus on the moderation role of past experience.

Li and Chen (2021) apply PLS-SEM in the e-commerce context by investigating how different promotion strategies of Online Shopping Festival may affect customer's intention to participate. This study identifies two types of online festival promotion strategies, namely, product promotion (Perceived Temptation of Price Promotion, Perceived Categories Richness of Promotion and Perceived Fun of Promotion Activities) and atmosphere promotion (Perceived Contagiousness of Mass Participation). Drawing from stimulus-response theory, contextualized model is developed to study how product promotion strategies and the atmosphere promotion strategy interact and affect customers' intention to participate in Online Shopping Festivals. Based on a sample of 495 consumers, PLS-SEM analysis showed that the four proposed product promotion and atmosphere promotion strategies all had significant positive impacts on consumers' intention to participate in the Online Shopping Festival. The moderation analysis showed that atmosphere promotion, operationalized as Perceived Contagiousness of Mass Participation, only positively moderated the relationship between of Perceived Temptation of Price Promotion and participation intention. The results and insights of this article would provide significant contributions for e-commerce platforms to improve their promotion strategies and enhance customer engagement during Online Shopping Festival.

Hsu et al. (2021) also investigate the e-commerce landscape with a special focus on the online-to-offline commerce. This article examines how customers' experience with online travel agencies (e.g. Booking.com) may affect their intention to patronize offline hotels. Drawing on the theory of reasoned action, Hsu et al. (2021) develop a model that studies the impacts of service quality, reputation, market share and customer satisfaction with online travel agencies on customers' intention to book and patronize offline hotels. This study compares customers in China and Indonesia and the results showed a significant difference between the customers in these two countries. While the booking intention of customers in China was affected by the size of the online travel agencies, the booking intention of Indonesia customers was affected by service quality. Hsu et al. (2021) not only contribute to the literature on multichannel integration by understanding the differences in customer behaviors in different countries, it also provides an example on how to employ permutation test, MICOM, PLS-MGA, PLSpredict and IPMA to conduct cross-country analysis.

The study by Zhang et al. (2021) trusts in the online health consultation context where patients pay for online health consultation services and communicate with physicians' online. Based on the generic framework of online trust, this study develops a conceptual model to investigate the factors affecting a patient's cognitive and affective trust in physicians' online, and how online trust affects patients' intention to choose a physician. Zhang et al. (2021) collected data from 507 potential users and performed a PLS-SEM analysis that showed that physicians' ability directly affected a patient's cognitive online trust, while integrity and benevolence of physicians directly impacted patients' affective online trust in the physicians. Both cognitive and affective online trust were found to positively affect patients' intention to choose an online health consultation service, and a positive interaction effect was found between these two variables in affecting patients' intention. This study fills in the research gap of little attention being paid to the ability of physicians in patients' decision-making. In addition, the results contribute to the literature by revealing how cognitive and affective online trust interact and affect users' intentions. Methodologically, the study provides a demonstration on moderation analysis in PLS-SEM.

PLS-SEM has evolved for decades (Shiau et al., 2019) and become a popular methodology worldwide (Khan et al., 2019). Originally, PLS-SEM is an essential analytical tool in social sciences research to explain and predict phenomena (Joreskog and Wold, 1982; Wold, 1982). For prediction, researchers using PLS-SEM have most often reported in-sample metrics such as the R2 and Q2 for in-sample metrics (eg. Shiau and Chau, 2016). To provide out-of-sample prediction assessment tools for PLS-SEM is also important (Hair, 2020). For example, the CVPAT (e.g. Liengaard et al., 2020) and PLSpredict (e.g. Shiau et al., 2020; Shmueli et al., 2016) are particularly well suited for executing out-of-sample prediction-oriented assessments and comparisons (Chin et al., 2021). Further, the community of PLS-SEM practitioners has recently seen a dizzying array of developments that promise to move our research practices in new directions, but also raise challenges in how to best apply them. The methodological and empirical articles in this special issue will greatly help to solidify the use of existing advanced practices of PLS-SEM and to extend the state-of-the-art. In many instances, the advances made in this issue point to important future research directions for the community.

PLSpredict (Shmueli et al., 2016) ushered in a new way of thinking for many SEM researchers by challenging them to consider the out-of-sample generalizability of their models. However, there are many open-ended ways in which PLSpredict can be applied and it has taken some time for the PLS community to formalize best practices that are compatible with existing research approaches. The article by Martínez-Caro et al. (2021) in this issue demonstrates one straightforward way in which researchers have interpreted PLSpredict, while Chin et al. (2021) examine wider causal-prediction criteria. Researchers would benefit from applying these methods to future-proof their research by ensuring its validity in other samples or future data. As our understanding of causal-predictive thinking solidifies, we can look forward to more innovations with PLSpredict in future, particularly if it borrows more of the predictive logic and principles from the fields of big data and data science.

Future works could distinguish between particular criteria of predictive quality such as sensitivity, specificity, precision and recall. Moreover, methodological advances could more finely identify which specific, constructs, paths or measurements of a PLS-SEM model are hampering better predictions. The article by Schuberth et al. (2021) on composites-of-composites reminds us that there are many popular practices in the PLS-SEM community of researchers that have gone critically unexamined. We call on the PLS-SEM methodologists to more thoroughly examine commonly found practices with a critical eye. Possible candidates for reappraisal or refinement include the choice of path or item weighting, calculating statistical power and necessary sample size of complex models, and more. Many articles in this issue focused on the contingency perspective management studies, which are often operationalized as moderation or multigroup analysis (Carranza Vallejo et al., 2021; Hsu et al., 2021; Li and Chen, 2021; Mutum et al., 2021; Zhang et al., 2021). There is clearly a great interest among researchers applying PLS-SEM to explore and confirm theoretical contingencies. It behooves methodologists to bring further nuance and power to strengthen this approach, by investigating more such issues as power analysis of moderated relationships, measurement quality and invariance of multigroup analysis, multilevel moderation and more. Moreover, the work by Richter et al. (2021) work on conditional analysis remind us that there are more novel ways of considering decision-making than regression-based techniques. We encourage more attempts to integrate or reconcile PLS-SEM approaches with the family of asymmetric conditional analysis that includes NCA, QCA, csQCA, fsQCA and more.

In additional to the scope of this special issue, we recommend two addition directions for future development of PLS-SEM: (1) meta-analysis and (2) power analysis. Meta-analysis is a method to combine findings across studies and to accumulate theoretical knowledge in behavioral and social science. As individual studies have different results for a relationship, the application of meta-analysis is a powerful tool to solve the conflicting findings by statistical significance testing in analyzing and interpreting large data. The large numbers of studies represent their populations and yield parameter estimates that are close to the real (population) values. Thus, the results of meta-analysis show consistent outcomes of casual relationships. The meta-analysis has evolved for decades. Traditional meta-analysis relies on correlations. As SEM is a frequently used multivariate technique for testing hypothetical models in behavioral and social science, meta-analytic structural equation modeling (MASEM), which involves the techniques of synthesizing correlation matrices and fitting SEM (Cheung, 2008; Cheung and Chan, 2005), has been applied in many disciplines. However, MASEM is a covariance-based SEM approach and could not be applied for PLS-SEM methods. It is urgent to develop a meta-analytic PLS-SEM method to synthesize the results of PLS-SEM. Researchers may try to find a novel solution for meta-analytic PLS-SEM in the near future.

Although power analysis has long been recognized as important in business statistics, it has received scant attention from the researchers. Statistical power is the probability of correctly rejecting the null hypothesis when it is false (Cohen, 1988). If the power of the statistical test is low, seldomly will the null hypothesis get rejected and there is a high chance that a false theory will be accepted (i.e. Type II error). For researchers, they should not only care about avoiding Type I error but also pay attention to Type II error. Although many statistical power analyses have been developed for SEM during the last decades (McQuitty, 2004), seldomly have these analyses been applied in extant studies (Mertens and Recker, 2020). Moreover, most statistical power analyses are developed for covariance-based SEM but not for PLS-SEM, which calls for the development of more statistical power analyses for PLS-SEM. For empirical studies applying PLS-SEM, we recommend the application of statistical power analyses to ensure the validity of data analysis results. In summary, we hope the studies contained within this special issue creates a foundation for greater leaps in PLS-SEM methodology while also strengthening the rigor of applied studies that seek to employ these advances.

The guest editors would sincerely thank Professor Alain Chong and Professor Hing Kai Chan, Editor-in-Chiefs of Industrial Management & Data Systems (IMDS) for giving the authors the opportunity to explore the advanced issues in PLS path modelling for business and information systems research. This special issue is also supported by Zhejiang providence, China (Grant no. QJC1902003) and National Natural Science Foundation of China (Grant no. 72032008).

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