The Use of Partial Least Squares Structural Equation Modeling and Complementary Methods in International Management Research.

VerfasserRichter, Nicole F.

1 Introduction

Research in international business and management (IM) has its inherent challenges that, in turn, demand the application of fitting analytical methods. First, it is characterized by high complexity, which emerges from, among other factors, cross-border and cross-cultural relationships and differences in international environments, organizations and individuals under study (e.g., Cuervo-Cazurra et al., 2016; Eden & Nielsen, 2020). Second, it spans various subfields, such as economics, strategy and organizational behavior, and most theories draw on these subfields and are not unique to IM. As a result, a unified understanding is often missing, and it is not uncommon that research draws on different theoretical lenses to study the same phenomena. Accordingly, conducting research that advances theorizing and the development of overarching theories that uniquely clarify IM phenomena remains a crucial challenge (e.g., Knight et al., 2022; Oesterle & Wolf, 2011; Seno-Alday, 2010). Third, to ensure relevance IM research must be contextualized. That is, researchers face the challenge of contextualizing general (abstract) theoretical knowledge to particular IM settings, such as different institutional environments or cultures or to demonstrate that their findings and theories are context-free (e.g., Meyer, 2013; Tsui, 2007).

Selecting and applying analytical methods, therefore, must fit the complexity of the IM phenomena studied, enable development or refinement of IM theory and assessment of alternative theoretical lenses, and allow accounting for the contextual specifics that define IM phenomena. In light of such challenges, recent IM literature attests to the requirement of utilizing more sophisticated research designs and methodologies. For instance, proposed solutions revolve around the need to apply analytical techniques that allow comparative testing of alternative theoretical models and explanations, and to leverage method triangulation to name a few (e.g., Aguinis et al., 2020; Cuervo-Cazurra et al., 2017; Eden & Nielsen, 2020; Fainshmidt et al., 2020; Knight et al., 2022; Nielsen et al., 2020; Richter & Hauff, 2022).

Our purpose is not to repeat the solutions already proposed, but to further clarify whether and how researchers using partial least squares structural equation modeling (PLS-SEM) can address (some of) the challenges in IM research (see Fig. 1). We explain how research in IM can benefit from the capabilities that PLS-SEM offers; either as a stand-alone method or in triangulation efforts that leverage complementary approaches. While we provide a broad overview that serves as a foundation, we specifically outline opportunities to complement PLS-SEM research designs with qualitative data analyses (see Sinkovics et al., 2022 in this focused issue) and techniques such as fuzzy set qualitative comparative analyses (see Zhang et al., 2022 in this focused issue) and necessary condition analyses (see Bolivar et al., 2022 in this focused issue). In addition, we refer to important PLS-SEM capabilities that allow IM researchers to deal with some of the challenges they face in conducting their research. We will elaborate on recent advancements in PLS-SEM to test and compare alternative models using model fit criteria (see Cho et al., 2022 in this focused issue), and to assess complex relationships like moderated mediation (see Fredrich et al., 2022 in this focused issue).

2 Capabilities of PLS-SEM and Their Use in IM

IM has a long history of using structural equation models (e.g., Hult et al., 2006). In recent years, IM researchers increasingly appreciated the use of PLS-SEM, and there is further potential in the method that can be tapped by researchers in the field (Richter et al., 2016a, c).

PLS-SEM went through a quite typical "method life-cycle" (Bergh et al., 2022) from its invention in the 1980s to today: Wold (1982) developed PLS-SEM, which Lohmoller (1989) further extended. In the early phase of PLS-SEM, much of the discussion focused on comparisons with the statistically different covariancebased SEM (CB-SEM) approach (Sarstedt et al., 2016). Over time, PLS-SEM has emancipated itself from CB-SEM (Rigdon, 2012, 2014; Sarstedt et al., 2014). Today, in line with the early ideas of Joreskog and Wold (1982), who have introduced both CB-SEM and PLS-SEM, the two methods are seen as complementary rather than competing (Rigdon et al., 2017). PLS-SEM is acknowledged as being suited for identifying important explanators in models (e.g., sources of competitive advantage) and for predictive research since the method aims to reduce (improve) the residuals (explanation) of dependent indicators and constructs in the model (Dash & Paul, 2021; Richter et al., 2016a). It has become a well-established method that is used in a variety of disciplines (Hair et al., 2022). The publications of textbooks (e.g., Hair et al., 2018; Ramayah et al., 2018) and "how to" articles (e.g., Cheah et al., 2021; Hair et al., 2019), several review articles on the use of the method and special issues in different disciplines (see Table 1.1 in Hair et al., 2021), and impactful research networks (Khan et al., 2019; Rudiger et al., 2021) have contributed significantly to the awareness and dissemination of PLS-SEM. Its adoption has also been triggered by the availability of open-source packages in the statistical software R (such as cSEM, matrixpls and SEMinR) and various commercial applications such as WarpPLS, XLSTAT, and SmartPLS, with SmartPLS being particularly popular among users due to its rich functionalities and ease of use (Memon et al., 2021; Sarstedt & Cheah, 2019).

PLS-SEM is moreover still profiting from advancements (e.g., predictive model assessment in PLS-SEM; Sharma et al., 2022; Shmueli et al., 2019) put forward by a dynamic field of researchers who are enthusiastic about the method (see also Sarstedt et al., 2022a who provide an overview of advances in PLS-SEM). For researchers in IM and other disciplines who are users rather than developers of research methods, it can be difficult to keep up with these constant advancements and stay abreast of the potential benefits they can bring to their discipline. To bridge this gap in knowledge transfer, we will discuss selected advanced capabilities of PLS-SEM and outline their value for IM researchers more specifically (see Table 1).

Moreover, to understand whether researchers in IM are using the most advanced capabilities, we followed Cho et al. (2022) who reviewed six leading IM journals (Management International Review, International Business Review, Journal of International Management, Journal of World Business, Journal of International Business Studies, and Global Strategy Journal) from 2013 to September 2021 for studies that have applied PLS-SEM and identified N = 84 studies. We will refer to this set of articles to provide insights into the usage of PLS-SEM capabilities and triangulations with PLS-SEM (see Table 1). In addition, we discuss two topics in more detail which are of particular relevance for this focused issue.

Moderated (conditional) mediation analysis is often overlooked (e.g., Cheah et al., 2021; Hair et al., 2019) but provides an important basis for analyzing a variety of interesting research questions in IM. This kind of analysis, that simultaneously accounts for mediated and moderated relationships, enables better understanding how processes amplify or weaken or under which conditions they take place, which is not the case when mediation and moderation are tested independently. Although many researchers across a variety of business disciplines, including IM, still rely on regression analyses - as done in PROCESS. This however has been subject to considerable criticism: there is no need to use PLS-SEM and PROCESS in tandem (Sarstedt et al., 2020). Instead, as Cheah et al. (2021) outline, moderated (conditional) mediation analysis can be carried out in PLS-SEM and these advances provide an essential technique to better deal with the complexities that characterize IM. When IM researchers perform a moderated mediation analysis, they are advised to a priori form a clear and robust theoretical understanding for the moderated (conditional) mediating effect for first-stage moderation, second-stage moderation, or first- and second-stage moderation (Borau et al., 2015). That is, each moderation path (e.g., first-stage and/or second stage) in a mediation model must be supported by and consistent with the theoretical framework that underpins the IM study.

Mediated relationships may not be moderated by a single exogenous variable but instead be moderated simultaneously by two exogenous variables. This is addressed in the focused issue paper by Fredrich et al. (2022). Their paper on 'Dynamic Capabilities, Internationalization and Growth of Small- and Medium-sized Enterprises: The Roles of Research and Development Intensity and Collaborative Intensity' illustrates an advanced application of PLS-SEM by testing a second-stage threeway moderated mediation. Their study addresses the relationship between an SME's corporate-level dynamic capabilities and its growth via internationalization (i.e., the SME's export intensity). The authors analyze whether and how the effect of internationalization on growth depends simultaneously on a firm's research and development intensity and its collaborative intensity considering an interaction between both moderators. Their results indicate a positive impact of internationalization provided that research and development intensity and collaborative intensity are proportional. In contrast, when they are disproportional, SMEs do not experience positive marginal growth. Importantly, while the authors outline the results using the well-established two-dimensional three-way plot, they further clarify the results of the second-stage three-way moderation analysis by describing and interpreting the regions of significance...

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