Testing IB theories with meta-analytic structural equation modeling: The TSSEM approach and the Univariate-r approach
Abstract
Purpose
The purpose of this paper is to illustrate how international business (IB) researchers can benefit from meta-analytic structural equation modeling (MASEM) by introducing a statistically rigorous approach (i.e. two-stage meta-analytic structural equation modeling or TSSEM) and comparing it with a conventional approach (i.e. the univariate-r approach). The illustration and comparison present a methodological overview of MASEM that will assist IB researchers in selecting an optimal method.
Design/methodology/approach
In this paper, the MASEM method is elaborated upon, and methodological issues are addressed, by comparing the TSSEM and the univariate-r approaches using an empirical illustration. In this illustrative example, which is based on transaction cost economics, the effects of a firm’s internal factors on its levels of commitment in an international entry strategy are examined.
Findings
The MASEM method can help IB researchers to test and build on IB theories by synthesizing findings in the extant literature because this method reflects the theoretical complexity of IB (e.g. intercorrelationships among factors). Comparing the two approaches of MASEM, it is found in this study that due to its statistical rigorousness TSSEM has methodological advantages in helping IB researchers test theoretical models.
Originality/value
This is the first study to introduce MASEM into the discipline of IB strategies. In this paper, the authors introduce an advanced research method and illustrate two ways of using it.
Keywords
Citation
Tang, R.W. and Cheung, M.W.-.-L. (2016), "Testing IB theories with meta-analytic structural equation modeling: The TSSEM approach and the Univariate-r approach", Review of International Business and Strategy, Vol. 26 No. 4, pp. 472-492. https://doi.org/10.1108/RIBS-04-2016-0022
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:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited
1. Introduction
As a method of searching for generalizations and heterogeneities within a body of literature, meta-analysis has become the dominant approach for international business (IB) researchers to quantitatively synthesize empirical findings. Following the maturation of the IB discipline, a variety of topics have been meta-analyzed, such as the choice of entry mode with a transaction cost perspective (Zhao et al., 2004), the impact of cultural differences on entry mode choice and multinational enterprises (MNE) performance (Magnusson et al., 2008) and national cultural indices (Taras et al., 2012). While these studies have advanced our knowledge about important IB research questions, conventional meta-analytic methods have been criticized for their lack of fitness for IB studies (Buckley et al., 2013). One reason given for this lack of fitness is that IB research objectives differ significantly from those of many other disciplines. Specifically, as a research method developed from the fields of education (Glass, 1976) and psychology (Schmidt and Hunter, 1977), a conventional meta-analysis is typically used to summarize and assess empirical findings relating to a single effect size (e.g. a correlation coefficient of two variables). While an investigation into individual factors may contribute, for example, by examining bivariate correlations (e.g. “associations between multinationality and performance” in Yang and Driffield, 2012), the aim in IB research is to explore the boundary conditions of a theory (e.g. the conditions of an association between variables) as well as to develop and test the causal linkages and theoretical logic of the theory (Bello and Kostova, 2012; Thomas et al., 2011). Conventional meta-analysis is a fine approach to use when investigating the moderating effects of features of a study (e.g. the year of publication, the country in which data were originally gathered), but does not address theoretical links such as mediation and causation of theoretical variables, which are in fact of considerable importance in IB research.
Addressing this limitation, a methodological integration of meta-analysis and structural equation modeling (SEM) is proposed, called MASEM. The aim in MASEM is illustrating the complicated logic and mechanisms of a set of theory-suggested associations among constructs and/or variables (Becker, 1992, 2009), thus enabling IB researchers to seek new insights into theoretical paradigms (Kirca et al., 2011) and to examine multiple permutations of predictors, mediators and outcomes (Bergh et al., 2016).
A popular approach to conducting MASEM is the univariate-r approach (Viswesvaran and Ones, 1995). In this approach a bivariate meta-analytic process is first employed to obtain a pooled correlation coefficient matrix (e.g. Hunter & Schmidt’s procedure or HSMA, Schmidt and Hunter, 2014), and an effect size (i.e. a correlation coefficient between two variables) in a cell of the pooled correlation matrix is then considered to be independent of effect sizes in other cells (i.e. the correlation coefficients of other pairs of variables) for estimating SEM models. With the matrix of the presumably independent effect sizes, univariate-r meta-analysts construct SEM models. This approach raises many statistical concerns such as:
it is difficult to calculate an appropriate sample size because primary studies included in a meta-analytic study have various sample sizes;
a pooled correlation matrix is very likely to include non-positive definite matrices that make SEM estimation problematic;
sampling errors in the pooled correlation matrix are not properly handled;
it is statistically problematic to use a correlation matrix as a covariance matrix in fitting structural equation models (Cheung and Chan, 2005); and
the assumption of independence among the pooled correlations of variables is not always theoretically appropriate (as will be elaborated upon in the next section).
To address these issues, we advocate a multivariate-r approach – two-stage meta-analytic structural equation modeling (TSSEM; Cheung, 2014) – which includes statistically superior procedures for pooling meta-analytic data sets as well as estimating structural equation models. In this study, we respond to three essential questions:
How may MASEM benefit IB research?
How does TSSEM differ from the univariate-r method?
How does TSSEM work?
We begin by discussing the first question with a brief illustration of MASEM. We then elaborate the advantages of TSSEM compared to the univariate-r method. With an empirical example, we demonstrate the difference between TSSEM and the univariate-r method, and address the third question to illustrate how TSSEM can advance IB theories.
By addressing these questions, the current study makes a number of important contributions to IB research. First, we introduce an advanced research method to IB research. Prior studies have introduced the univariate-r approach (Bergh et al., 2016); in our study, we introduce an advanced method (i.e. TSSEM) and explicitly illustrate its steps. While the TSSEM approach is known in the field of psychology (Cheung and Chan, 2005), our study benefits IB researchers by providing a methodological map with an IB research example. It delineates how TSSEM may help IB researchers contribute to the IB literature. We also elaborate differences between the univariate-r and the TSSEM approaches using an empirical example related to international entry mode choices and present findings that may update what previous IB meta-analyses have found. Previous studies explained variations among MASEM approaches (Landis, 2013), but our study explicitly illustrates TSSEM’s methodological advantages over, and differences from, the univariate-r approach. A deliberate summary of approaches and an empirical illustration with an IB research topic will help IB researchers make contributions by meta-analyzing the extant literature. Finally, we empirically compare the results of the two MASEM approaches, which will enable IB researchers to select an optimal means for conducting meta-analytic research.
2. Meta-analytic structural equation modeling
2.1 Conventional meta-analysis and MASEM
Meta-analysis is “the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings” (Glass, 1976, p. 3), while MASEM involves examining a body of literature with model specifications that illustrate “a set of postulated interrelationships among constructs or variables” (Becker and Schram, 1994, p. 358). In this sense, compared to a conventional meta-analysis, an important feature of MASEM is the investigation of associations among a group of variables suggested by a theoretical model.
While the concept of “models” appears in conventional meta-analyses as well as in MASEM studies, meta-analytic variables and theoretical explanations vary. For instance, a conventional meta-analytic study may employ “meta-regression” to examine the moderating effects of study features (Lipsey and Wilson, 2001). In the meta-regression model, a dependent variable is an effect size of a meta-analytic study, and independent variables are features of primary studies[1] (e.g. years of publication). The meta-regression model allows meta-analysts to understand the dynamics of moderating effects and explains the heterogeneity of a body of literature in a more rigorous manner than would be possible using a single categorical moderator variable. While effect sizes and study features are also investigated in MASEM, effect sizes can be dependent as well as independent variables and mediator variables. Together with moderator variables that represent study features, these four types of effect-size variables enable a more complicated theoretical model to be tested with MASEM than would be possible in a conventional meta-analytic study (Hafdahl, 2009; Joseph et al., 2007).
Several well-cited IB meta-analytic studies would have benefited from MASEM. An example is that of Zhao et al. (2004), which tested how transaction cost-related factors may influence choices of ownership-based entry mode. In their meta-analytic study, Zhao and colleagues separately investigated three transaction cost factors (i.e. asset specificity, internal uncertainty and external uncertainty). The separate investigation implies an assumption that the three factors have independent effects, which can be illustrated in Model A of Figure 1. This research design with the assumption of independency enabled Zhao et al. (2004) to search the literature on the heterogeneity of an individual effect (e.g. the effect of Advertising Intensity) and, consequently, to show what inconsistencies are to be found in the literature (e.g. various findings about the effect of Advertising Intensity among primary studies, Zhao et al., 2004).
However, when research questions become complex, and if IB researchers tend to reveal more complicated associations among a set of variables, a conventional meta-analysis may fall short. For example, if IB meta-analysts want to examine the determination of transaction cost-related factors simultaneously (i.e. remove the assumption of independence between these factors), they will need to consider a complex and more realistic model using MASEM. Model B in Figure 1 is an example. It is more consistent with the transaction cost economics (TCE) paradigm that suggests that a firm governs and monitors transactions (e.g. entry into a foreign market) by considering three transaction cost factors at the same time (Williamson, 1979, 1981). To reflect this theoretical complexity, IB researchers can choose one of the two MASEM approaches: univariate-r and multivariate-r (TSSEM).
2.2 Univariate-r and TSSEM
The univariate-r method is an ad hoc approach that combines a conventional meta-analytic method (e.g. HSMA) and the SEM method (Viswesvaran and Ones, 1995). Specifically, in a univariate-r study, HSMA is first to estimate a mean effect size (i.e. a meta-analytically averaged correlation coefficient) and this is treated as an element of a pooled correlation matrix. After all elements are obtained, the matrix is used to fit a structural equation model. Although HSMA and SEM are widely accepted research methods, a simple combination may not generate statistically rigorous results.
In addition, the TSSEM approach is developed according to the statistical theory of SEM, and includes two estimation procedures: maximum likelihood estimation (MLE), for pooling a correlation matrix, and weighted least squares (WLS), for estimating a structural equation model. We elaborate on the MLE and WLS of TSSEM in Section 3, and compare the univariate-r and TSSEM approaches below.
First, since different researchers independently conduct primary studies, it is likely that different numbers of correlation coefficients are reported in primary studies. The univariate-r method synthesizes correlation coefficients as if they were uncorrelated, and thus elements of a correlation matrix are computed individually. Similar to the separation investigation illustrated in Section 2.1, the assumption of independence is not consistent with that of many IB theories that suggest correlations among factors. However, the TSSEM approach synthesizes a correlation matrix with the multivariate approach by taking into account the dependence of the correlation coefficients. Several researchers have shown that the multivariate approach is more efficient than the univariate approach in synthesizing effect sizes (Jackson et al., 2011). Cheung (2015a) demonstrates that it is similar to the pairwise deletion in a data analysis if correlation coefficients are synthesized with the univariate-r method. The TSSEM approach uses a multivariate approach with MLE to synthesize correlation matrices. MLE outperforms approaches such as HSMA because MLE is preferred in handling missing data (Enders, 2010) and is unbiased and efficient when the data are missing completely or at random.
Another concern of univariate-r is the potential of non-positive definite matrices. When elements of a correlation matrix are calculated by pairwise deletion, i.e. the correlation coefficients are calculated independently of other correlation coefficients, the correlation matrix may be non-positive definite (Wothke, 1993), making the pooled correlation matrix no longer appropriate for SEM. Wothke (1993) recommends the use of MLE to handle the missing data, which minimizes the chance of non-positive definiteness. As such, the likelihood of encountering a non-positive definite pooled correlation matrix is less with the TSSEM approach than with the univariate-r approach.
Furthermore, when the univariate-r approach is used to fit structural equation models, the pooled correlation matrix is used as if it were a covariance matrix. As a result, the test statistics and the standard errors become problematic (Cudeck, 1989). In contrast, the TSSEM approach analyzes the correlation matrix with the WLS estimation, which provides correct test statistics and standard errors for IB meta-analysts (statistical details are present in Section 3).
Finally, since the elements of a pooled correlation matrix are usually based on different numbers of studies, users of the univariate-r approach have to calculate a harmonic mean[2] of these sample sizes and consider it to be an “estimated” sample size in fitting a structural equation model. As sample sizes for fitting structural equation models are usually very large in MASEM, some researchers have argued that regardless of what sample sizes are used in the analysis, the parameter estimates are still likely to be significant (Schmidt and Hunter, 2014). However, the objective of a meta-analysis (including a conventional meta-analytic study and an MASEM study) is to not only test the significance of parameter estimates, but also to check the appropriateness of proposed models and the precision of the parameter estimates (confidence intervals). Using different sample sizes may lead to different results and interpretations. For example, Bollen (1990) showed that a sample size is either explicitly or implicitly involved in calculating many goodness-of-fit indices. Cheung (2015a) demonstrates that if different sample sizes are used in fitting structural equation models, the precision of some of the pooled correlation matrices is overestimated, while the precision of others is underestimated. An arbitrarily chosen sample size also affects the test statistic, some goodness-of-fit indices (e.g. RMSEA), the standard errors and the confidence intervals of a structural equation model. This problem is not encountered when the TSSEM approach is used since in the TSSEM approach a weight matrix is used to improve the precision of estimates, as described below.
3. Two-stage structural equation modeling
Two stages are involved in a TSSEM study. In the first stage, a correlation matrix is pooled, and the pooled correlation matrix is used to fit structural equation models in the second stage. Similar to a conventional meta-analysis, TSSEM has two types of models: fixed- and random-effects models. In the fixed-effects model, it is usually assumed that the population effect sizes are homogeneous. Conditional inferences are provided to the studies included in the analysis. In the random-effects model, the homogeneity of effect sizes is not assumed and the intention is to provide unconditional inferences generalizing beyond the studies included in the analysis (Hedges and Vevea, 1998; Hunter and Schmidt, 2000). Since one of the objectives of an MASEM study is to generalize from findings beyond the extant literature, we illustrate the TSSEM method using the random-effects model[3].
3.1 Stage 1 analysis
When dealing with correlation matrices, it is easier to transform the correlation matrices into vectors. Suppose we have a symmetric matrix:
We may define a vector
where ρ_{i} and u_{i} are the population correlation vector and the study-specific random effects in the ith study, respectively. The model for the sample correlation vector r_{i} = vechs(R_{i}) in the ith correlation matrix R_{i} is:
where Cov(u_{i}) = T^{2} is the variance component of the study-specific random-effects and Cov(e_{i}) = V_{i} is the known sampling covariance matrix in the ith study. To fit the above model, Cheung (2015a) showed how the multivariate meta-analysis with MLE could be directly adopted here. The ML estimators have many desirable properties such as consistency, asymptotical un-bias, asymptotical efficiency and asymptotically normal distribution.
3.2 Stage 2 analysis
After the stage 1 analysis, a vector of the pooled correlation matrix ρ̂_{Random} and its asymptotic sampling covariance matrix V̂_{Random} are estimated. The pooled correlation vector represents the average of the correlation matrices of the population, while its asymptotic sampling covariance matrix indicates the precision of the estimated average correlation matrix.
According to Browne (1984), the weighted least square (WLS) discrepancy function used to fit the correlation structure model ρ(γ) is:
ρ_{Random} and V_{Random} are treated as observed values in the above equation. This approach is similar to that in a conventional meta-analysis, which takes the inverse of the sampling variance (i.e. V_{Random} in TSSEM) as the weight in calculating the average effect size. We should also note that the estimated variance component T̂^{2} in the stage 1 analysis is not directly included in the discrepancy function in the stage 2 analysis. Since V_{Random} is estimated after controlling for the random effects, it has already taken the random effects into account[4].
4. An illustration example
4.1 Overview
Our empirical example is extracted from a meta-analytic study (Tang et al., 2013), which synthesizes findings from 116 primary studies regarding the determination of commitment levels in the international entry strategy of firms. We use correlation coefficient matrices extracted from the 116 primary studies (112 articles[5]) to construct our MASEM data set, and illustrate both the univariate-r and the TSSEM approaches by answering an IB research question:
What internal factors determine a firm’s level of commitment to international entry?
The dependent variable “a firm’s commitment level” is coded as a dummy variable measured by considering a strategic decision in comparison with another[6]. For example, in comparison to a joint venture, a wholly owned subsidiary is defined as a decision involving a high level of commitment. In addition, we adapted the following eight manifest variables:
Technology and tacit know-how, which is measured by the firms’ R&D-related expenditures and experience, and marketing and training expenses (Brouthers and Dikova, 2010);
Business diversity, which represents whether or not a firm has business in more than one industry (Estrin et al., 2009);
Management and operation experience, which indicates a firm’s management and operational experience gained in its domestic market and representing the firm’s internal management skills. It is measured by integrating proxies such as years after being established and membership of an industrial group (e.g. Fortune 500) (Prashantham, 2011; Richards and Yang, 2007);
Firm size, which is measured by synthesizing proxies including total sales, assets and number of employees (Brouthers et al., 2003; Paul and Wooster, 2008);
General international experience, which means the knowledge accumulated from prior experience via international activities, formed by synthesizing proxies such as the number of countries from which a firm has IB partners, years of having IB and the proportion of foreign assets that a firm has (Kogut and Zander, 1993; Lu, 2002);
International decision-specific experience, which indicates the experience of making strategic decisions related to international entry, and is mainly measured by operationalizing measures such as the number of years of using an international entry strategy and the number of different strategies being used (Malhotra et al., 2011; Padmanabhan and Cho, 1999);
International market knowledge, which represents a firm’s experiential knowledge in host countries, measured by years of business, total sales and the number of subsidiaries in a host country (Barkema and Vermeulen, 1998; Li and Meyer, 2009; Slangen, 2013); and
International strategy, which is measured by a dummy variable of 1 for a global-oriented strategy (e.g. cost leadership strategy in Davis et al., 2000; intention of global integration in Luo, 2001) and 0 for a local-focused strategy (e.g. product differentiation strategy in Davis et al., 2000; resource-seeking strategy in Gil et al., 2006).
Sample sizes of the dependent variable and these manifest variables are shown in Table I. These manifest variables allow us to construct latent variables of a structural equation model that is suggested by the TCE paradigm. To compare the two approaches of MASEM, we first demonstrate the univariate-r approach and then the TSSEM approach, after briefly introducing TCE.
4.2 TCE paradigm
The key consideration of TCE is to minimize costs in international investment activities. It is suggested that a transaction has three core attributes: Asset Specificity, Internal Uncertainty and External Uncertainty (Williamson, 1979, 1985). These three attributes are also deemed to have major impacts on a firm’s international decisions (Zhao et al., 2004), suggesting that there are three latent variables in a structural equation model. In illustrating the two MASEM approaches, the impact of internal factors (i.e. Asset Specificity and Internal Uncertainty) only are investigated in this empirical example.
First, as Asset Specificity relates to a broad range of resources and to a firm’s ability to differentiate its strategy and performance, the latent variable Asset Specificity can be reflected by four manifest variables: Technology and tacit know-how, Business diversity, Management and operational experience, and Firm size.
Another latent variable is Internal Uncertainty. In the TCE paradigm, Internal Uncertainty comes from the difficulty of assessing an agent’s performance and deficiency in a firm’s experience, suggesting the following composition of manifest variables: General international experience, International decision-specific experience, International market knowledge and International strategy.
4.3 Univariate-r method
Following a typical univariate-r procedure (Viswesvaran and Ones, 1995), we computed the corrected correlation coefficients between the dependent variable (i.e. the commitment level) and the manifest variables, with Stata’s “metan” package (Harris et al., 2008). Then, we pooled the bivariate correlation coefficients into a meta-analytic matrix for estimating a structural equation model. Table II displays the corrected correlation coefficients and their corresponding confidence intervals.
We also calculated a harmonic mean (see Footnote 2 in Section 2.2) and used it as the sample size for estimating the structural equation model of TCE. We then employed the SEM function of Stata 13 and obtained the univariate-r model shown in Figure 2, with goodness-of-fit indexes including χ^{2} = 513 (df = 25, p-value = <0.001), RMSEA = 0.122, SRMR = 0.079, TLI = 0.383 and CFI = 0.572.
4.4 TSSEM method
Following the two-stage procedure discussed in the preceding section, at the first stage, we estimated a pooled correlation matrix via a random-effects model that also provides a sampling covariance matrix of the pooled correlation coefficients. Table III shows the pooled correction coefficients of the dependent variable and the manifest variables.
Then, we fitted the TCE model again, using an R software package “metaSEM” (Cheung, 2015b). Figure 3 displays the model estimated using the TSSEM method. This model presents a better goodness-of-fit; i.e. χ^{2} = 59.473 (df = 25, p-value = <0.001), RMSEA = 0.002, SRMR = 0.061, TLI = 0.857[7] and CFI = 0.901. A comparison of the results of the univariate-r and TSSEM approaches is given in Table IV.
4.5 Results of univariate-r and TSSEM
A comparison of Tables II and III shows that different results were obtained from the first stages of the univariate-r approach and the TSSEM approach. For example, the corrected correlation coefficient between Firm size and Commitment Level is -0.016 (p < 0.05) from the univariate-r approach, indicating a significant and negative relationship between a firm’s size and its level of commitment. However, the coefficient of the same pair of variables is 0.057 (p < 0.05) from the TSSEM, suggesting a positive association. This divergent result not only comes from methodological differences between the univariate-r and the TSSEM approaches, but leads to different model estimations and varying substantive interpretations as well.
Turning to Figures 2 and 3, we note that the two models offer contradictory findings. In Model 1 (the univariate-r approach in Figure 1), both Asset Specificity and Internal Uncertainty exert negative impacts on a firm’s decision with regard to its level of commitment (v1), but Model 2 (the TSSEM in Figure 3) shows positive effects. Given non-significant coefficients of Asset Specificity and Internal Uncertainty in both models, we cannot argue that either model is convincing. This suggests that a better approach in the future would be to test External Uncertainty together with Asset Specificity and Internal Uncertainty, and to examine the model fit for evidence. It should be noted that there is an improper correlation between Asset Specificity and Internal Uncertainty in Figure 2 (i.e. −2.10), implying possible issues with the univariate-r approach and suggesting that we consider further studies, as discussed below.
5. Implications and discussion
5.1 Contributions and implications
In this study, we discussed how MASEM can facilitate IB research, and elaborated on its two methods: the univariate-r and the TSSEM approaches. While the univariate-r approach has been widely used (Bergh et al., 2016; van Essen et al., 2012), the TSSEM approach – a methodological update of MASEM – is as yet unknown in IB research. We advocate the use of the TSSEM approach because its fundamental assumption (i.e. the interdependence of pooled effects) is in alignment with IB theories that suggest that many theoretical elements are not independent. Our study illustrates how IB researchers may apply this statistically and theoretically updated method to solve their research questions. Prior applications of MASEM to the testing of theoretical models focused on an intuitive means that brought a huge volume of knowledge to the IB discipline. Our methodological illustration of TSSEM contributes by proposing and demonstrating an alternative way of supporting IB meta-analysts.
As an illustration, the empirical example in our study examines how a firm’s level of commitment in international strategic activities can be determined, and we contribute to the IB literature by explicitly showing the effects of asset specificity and internal uncertainty in this IB strategy decision. Given its non-significant influence in the models, a further meta-analytic study that includes external uncertainty in the current model will make extra contributions.
In addition to the TCE paradigm and the entry mode literature, IB researchers may benefit from MASEM approaches by searching for answers to many IB research questions. For example, culture and cultural distance have been meta-analyzed using conventional methods that provide evidence on relationships between culture and other IB strategy elements (e.g. international diversification, MNC performance in Magnusson et al., 2008; Tihanyi et al., 2005). Meta-analytic findings of these relationships may be updated using MASEM approaches by, for instance, examining the mediating effects of cultural distance. Specifically, theoretical contributions could be made by investigating how international diversification influences the cultural dynamics of MNCs (i.e. through a combination of multiple cultural distances between headquarters and foreign subsidiaries as well as those between foreign subsidiaries), and consequently how the cultural dynamics may affect the performance of MNCs. Moreover, IB meta-analysts may also make contributions by employing MASEM approaches to analyze some research questions that have not previously been meta-analyzed, such as the influences of institutional environments (e.g. a comparison between developed countries and emerging economies) and the impacts of innovation on internationalization.
5.2 Limitations and directions for future research
We note several limitations that provide directions for future research. First, although as many primary studies as possible were included in our empirical illustration, not enough freedom was gained to satisfy the data consumed by MASEM (both the univariate-r and the TSSEM approaches) in examining a moderating effect (e.g. to divide primary studies into two groups and estimate two structural equation models separately). Because of the complex nature of IB theoretical models (e.g. even though it does not directly investigate a phenomenon at three levels – country, industry and firm – an IB study normally implies a three-level analysis), an IB MASEM study may involve a large number of theoretical elements and require more data than a conventional study. Specifically, a conventional meta-analysis requires six correlation coefficients to examine Model A in Figure 1, and a MASEM study needs 15 (i.e. 5 × (5 + 1)/2 = 15) correlation coefficients to test Model B in Figure 1 because of the demands of a pooled correlation matrix. This seems to imply that IB researchers should select only mature topics on which a huge number of primary studies have been conducted, because this will help the researchers to find statistical and theoretical meanings. A possible solution is to include articles that are not related to IB, but that report statistics on variables that IB meta-analysts would like to investigate. For example, Kirca et al. (2011) analyzed the multinationality and performance of firms by including 111 studies published not only in IB and management journals, but in finance journals as well. Likewise, Taras et al. (2012) synthesized findings from 451 primary studies, many of which were not published in IB journals. However, a cross-disciplinary and comprehensive coverage of primary studies implies that IB meta-analysts should put more effort into conducting a MASEM study than a conventional study. Another concern arises from the comparability of findings across different fields. If the findings of the included studies are derived from different conceptual constructs, a simple combination of findings may not theoretically support meta-analytic results. As such, IB researchers may need to ensure that the included studies are estimating the same constructs of interest.
Some meta-analysts prefer to correct for such statistical artifacts as unreliability (Alliger, 1995), and a TSSEM study can also use correlation matrices corrected for unreliability. After reviewing MASEM studies published between 2000 and 2011, Michel et al. (2011) found that conclusions based on corrected and uncorrected correlations were similar. However, the empirical performance in simulation studies remains unknown, which suggests that future studies need to be conducted to address whether the after-corrected effect sizes perform as well as the uncorrected correlations.
Another concern arises from the sources of a pooled correlation matrix. Some meta-analysts extract a matrix from an existing meta-analytic study (i.e. the matrix used in our empirical illustration) for a new MASEM study (Eisend, 2011), and many others combine meta-analytically derived correlations from different studies to form a pooled correlation matrix. The second approach may introduce additional complications because the correlation coefficients are based on different inclusion criteria and meta-analytic models. It remains unclear whether the second approach is statistically justified. Given the uncertainty of MASEM methodology, IB meta-analysts need to be aware that there may be trade-offs between methods.
5.3 Strengths and boundaries of MASEM for IB research
While meta-analysis allows for primary research findings to be synthesized and cumulated into a single effect size that demonstrates the magnitude and directionality of the relationships between variables (Schmidt and Hunter, 2014), MASEM advances the conventional meta-analytic method by integrating multiple effects into a single model with statistical information about the model (e.g. Goodness-of-fit). With an integrated model, MASEM can investigate indirect effects with mediator variables and compare models suggested by different theoretical perspectives (as elaborated in Section 5.1). In particular, when a MASEM study includes all findings from the extant literature regarding a set of particular relationships, IB researchers can maximize the external validity of the study (Shadish et al., 2002) and obtain more powerful statistical evidence than would be possible in a single primary study (Cheung and Chan, 2005). This enables IB researchers to test frameworks with new theoretical constructs using latent variables and identify new directions in the development of a theory.
MASEM is subject to some boundary conditions that all meta-analytic methods may have, such as an inability to analyze emergent topics on which adequate primary studies have yet to be conducted, and a tendency to arrive at weak conclusions due to the poor quality of the primary studies. Also, due to its theoretical-model-driven nature, the validity of MASEM may be affected by three limitations.
First, MASEM may not test a specific model where primary studies that provide sufficient observations for one or more theoretical elements (e.g. variables, correlations) are lacking. Although statistical techniques such as MLE may handle study-level missing values to a certain degree (Cheung, 2015a), and the comprehensive coverage of primary studies may also reduce the influence of study-level missing values, a synthesis-level missing value may make the investigation of a theoretical model impossible (Becker and Schram, 1994)[8]. In this sense, it would be unwise to completely rely upon MASEM to test new IB theories. IB researchers may conduct primary studies to test new theories, and allow MASEM studies to complement primary studies to advance and enhance existing theories.
Also, difficulties have been encountered with using MASEM to test continue moderators at the synthesis level. Currently, moderating effects can be examined with categorical moderator variables (e.g. US vs non-US studies) by splitting a meta-analytic data set into two (or more) sub-data sets (e.g. a US data set and a non-US data set). Sub-group models can then be estimated, and a comparison of the sub-group models may reveal that the categorical moderator has moderating effects. However, continue moderators (e.g. years of publications) may constrain the ability of IB meta-analysts to carry out the above processes.
Finally, IB meta-analysts may not draw inferences from a causal model, unless all primary studies included in a meta-analytic study were conducted with experimental designs (Becker and Schram, 1994; Bergh et al., 2016; Landis, 2013), because causality is established upon the following conditions: “the cause preceded the effect, the cause was related to the effect and we can find no plausible alternative explanation for the effect other than the cause” (Shadish et al., 2002, p. 6). However, the majority of IB studies, if not all of them, do not use experimental designs. Thus, IB researchers have to scrutinize meta-analytic models by considering them to be “explanatory models” (Becker and Schram, 1994). An explanatory model does not have strict requirements on causal inferences, but allows IB meta-analysts to take advantage of MASEM and uncover unique associations among key elements of a theory.
6. Conclusion
This study introduced an advanced meta-analytic method (i.e. MASEM) to the IB literature by comparing two approaches: univariate-r and TSSEM. Following the conventional MASEM strategy (i.e. stage 1 – pooling a meta-analytic correlation matrix, and stage 2 – fitting the matrix in a structural equation model), the TSSEM approach advances the first stage with an MLE computation and the second stage with a WLS estimation, which ensures a rigorous process for IB researchers to follow when conducting a meta-analysis. Our empirical example examines a long-debated topic in the field of IB strategies, and finds exploratory evidence using a comprehensive model based on the TCE paradigm. It is our hope that this paper will encourage IB researchers to conduct MASEM using the TSSEM approach and contribute new insights to the IB literature.
Figures
The number of studies and the accumulative sample size^{a}
Variables | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
Commitment level | 19,728 | 3,616 | 17,802 | 31,060 | 51,355 | 134,246 | 148,093 | 3,273 | |
Technology and tacit know-how | 34 | 1,031 | 10,726 | 23,434 | 18,831 | 8,982 | 12,876 | 1,991 | |
Business diversity | 7 | 4 | 1,171 | 2,418 | 1,106 | 754 | 3,675 | 277 | |
Management and operation experience | 21 | 12 | 1 | 17,659 | 12,698 | 9,765 | 4,007 | 703 | |
Firm size | 49 | 34 | 4 | 15 | 43,532 | 14,039 | 15,969 | 2,122 | |
General international experience | 47 | 28 | 2 | 14 | 40 | 30,237 | 18,347 | 4,121 | |
International decision-specific experience | 14 | 12 | 3 | 6 | 12 | 12 | 113,591 | 160 | |
International market knowledge | 39 | 23 | 7 | 5 | 25 | 24 | 11 | 812 | |
International strategy | 12 | 7 | 1 | 2 | 8 | 11 | 1 | 5 |
This table summarizes the information extracted from 116 primary studies (matrices); The triangle to the lower left of the diagonal contains the number of studies (n); The triangle to the upper right of the diagonal shows the cumulative sample size (N)
Pooled correlation coefficients and the population variability for the Univariate-r approach^{a}
Variables | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
Commitment level | (0.075, 0.103) | (−0.032, 0.033) | (−0.114, −0.085) | (−0.027, −0.005) | (0.040, 0.057) | (−0.023, −0.013) | (−0.052, −0.042) | (−0.026, 0.042) | |
Technology and tacit know-how | 0.089 | (−0.153, −0.031) | (0.017, 0.054) | (0.094, 0.120) | (0.091, 0.120) | (0.075, 0.116) | (0.016, 0.050) | (−0.077, 0.001) | |
Business diversity | 0.001 | −0.092 | (−0.006, 0.082) | (0.309, 0.389) | (−0.068, 0.168) | (−0.003, 0.141) | (0.172, 0.237) | (−0.199, 0.038) | |
Management and operation experience | −0.100 | 0.036 | 0.038 | (0.246, 0.276) | (0.024, 0.058) | (0.444, 0.484) | (0.219, 0.281) | (−0.040, 0.273) | |
Firm size | −0.016 | 0.107 | 0.349 | 0.261 | (0.199, 0.217) | (0.159, 0.193) | (0.338, 0.369) | (−0.084, 0.001) | |
General international experience | 0.048 | 0.106 | 0.050 | 0.041 | 0.208 | (0.077, 0.100) | (0.293, 0.322) | (0.039, 0.100) | |
International decision-specific experience | −0.018 | 0.096 | 0.069 | 0.464 | 0.176 | 0.089 | (0.028, 0.039) | (−0.053, 0.260) | |
International market knowledge | −0.047 | 0.033 | 0.205 | 0.250 | 0.354 | 0.308 | 0.034 | (−0.163, −0.024) | |
International strategy | 0.008 | −0.038 | −0.080 | 0.116 | −0.042 | 0.069 | 0.103 | −0.093 |
This table synthesizes effect sizes from 116 primary matrices; The parentheses in the variables column show how the variables are measured; The triangle to the lower left of the diagonal contains the corrected correlation coefficients; The triangle to the upper right of the diagonal shows the 95% confidence interval of the corresponding correlation coefficients
Pooled correlation coefficients and the population variability for the TSSEM^{a}
Variables | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
Commitment level | 0.011** | 0.010 | 0.024** | 0.025*** | 0.020*** | 0.040* | 0.036*** | 0.050* | |
Technology and tacit know-how | 0.106*** | 0.019 | 0.005 | 0.037*** | 0.014*** | 0.019* | 0.023** | 0.044^{a} | |
Business diversity | −0.043 | −0.094 | 0.000 | 0.020 | 0.003 | 0.000 | 0.029^{a} | 1.000 | |
Management and operation experience | −0.029 | 0.037 | 0.038 | 0.049** | 0.013* | 0.056^{a} | 0.035 | 0.000 | |
Firm size | 0.057* | 0.090** | 0.218** | 0.274*** | 0.028*** | 0.016* | 0.037** | 0.033 | |
General international experience | 0.077*** | 0.065** | 0.155** | 0.110** | 0.282*** | 0.071* | 0.054*** | 0.010 | |
International decision-specific experience | 0.024 | 0.054 | 0.057 | 0.234* | 0.185*** | 0.270*** | 0.106* | 0.000 | |
International market knowledge | 0.004 | 0.072* | 0.066 | 0.225** | 0.287*** | 0.303*** | 0.150 | 0.006 | |
International strategy | 0.020 | −0.048 | −0.054 | 0.106** | −0.066 | 0.068^{a} | 0.092 | 0.094^{a} |
This table synthesizes effect sizes from 116 primary matrices; The parentheses in the variables column show how the variables are measured; The triangle to the lower left of the diagonal contains the pooled correlation coefficients (r’s); The triangle to the upper right of the diagonal shows the Tau2’s of the corresponding correlation coefficients;
p < 0.10;
p < 0.05;
p < 0.01;
p < 0.001
Comparison of model fit^{a}
Index | Model 1: univariate-r method | Model 2: TSSEM method |
---|---|---|
χ^{2} | 513.000 | 59.473 |
df | 25.000 | 25.000 |
p-value | <0.001 | <0.001 |
RMSEA | 0.122 | 0.002 |
SRMR | 0.079 | 0.061 |
TLI | 0.383 | 0.851 |
CFI | 0.572 | 0.901 |
AIC | 32947.514 | 9.473 |
BIC | 33097.758 | −249.674 |
df – the degree of freedom; RMSEA – the root mean square error of approximation; SRMR – Standardized root mean squared residual; TLI – the Tucker-Lewis index; CFI – Comparative fit index; AIC – the Akaike Information Criterion; BIC – the Bayesian Information Criterion
Notes
“Primary studies” refer to studies that are meta-analyzed by a meta-analytic study.
The harmonic mean is: k/[Σ(1/N_{i})], where k is the number of meta-analytic effect sizes, and N_{i} is the total sample size of each primary study.
Readers interested in the fixed-effects TSSEM approach may refer to Cheung (2015a).
The metaSEM package in R can facilitate the implementation of this procedure.
A list of references is available upon request. We initially obtained 118 primary studies from 114 articles that reported correlation matrices, but retained only 116 studies because non-positive definite matrices were found in two studies of two articles. While the univariate-r approach does not consider a non-positive definitive matrix, the TSSEM method recommends avoiding it. We included only the positive definitive matrices in this empirical example to demonstrate both methods in a comparable way.
In TSSEM practice, continuous dependent variables are preferred to binary variables.
TSSEM’s TLI and CFI indexes are relatively smaller than the optimal value (e.g. 0.95) because TLI and CFI need a baseline model for a comparable computation. Yuan and Chan (2005) have shown that the values of these indexes, such as TLI and CFI, can be quite different depending on the estimation methods, e.g. the WLS vs the MLE. Cheung (2015a) and Cheung and Chan (2009) have suggested that RMSEA and SRMR are more stable for use in assessing model fit in MASEM.
A study-level missing value may appear when some primary studies provide the relationship of a pair of variables and others do not. A synthesis-level missing value appears when the relationship of one pair of variables has not been examined in any eligible primary studies, although the variables are components of a theoretical model.
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