Abstract
Since the 1970s, structural equation modeling (SEM) has been applied for the analysis of causal relationships in economic and social sciences (Götz and Liehr-Gobbers 2004: 714; Henseler 2005: 70; Herrmann et al. 2006: 35). SEM is a multivariate statistical technique that – by integrating different regression- and factor-analytic methods – allows the testing and estimation of theoretically derived, casual relationships between variables (Bortz 1993: 436; Rigdon 1998: 251). Its high popularity in economic and social sciences is mainly attributed to two factors. First, it is the only multivariate statistical method that allows one to simultaneously assess the quality of construct measurement in terms of reliability and validity on the one hand, while on the other hand estimating the strength of a relationship between constructs (Backhaus et al. 2008: 511; Henseler 2005: 70). Second, SEM enables scientists to measure not only observable (manifest) variables, but also unobservable (latent) variables (Chin 1998b: 296; Chin and Newsted 1999: 307; Herrmann et al. 2006: 35; Rigdon 1998: 251). As latent variables are very common in economic and social sciences, the ability to model latent variables is of particular importance (Chin 1998b: 296). Due to the fact that latent variables cannot be observed directly, they are assigned manifest variables – which can be derived empirically and measured on the basis of metric scales – in a measurement model (or outer model) (Backhaus et al. 2008: 513; Henseler 2005: 70), as illustrated in Fig. 3.1
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Notes
- 1.
The independent variables are termed exogenous, as their causes lie outside the structural model, while the endogenous variables are determined by variables within the structural model (Bollen 1989: 12). The characteristics of structural models and measurement models, as well as the applied nomenclature in Fig. 3.1, will be explained in more detail in Sects. 3.2.1 and 3.2.2.
- 2.
As SEM is regarded as an extension of first-generation approaches, any constraints or assumptions that limit its application would set it back to a first-generation procedure (Chin and Newsted 1999: 308).
- 3.
While using highly correlated measures as independent variables in regression analyses leads to multicollinearity (Homburg 1992: 499), in SEM – as correlated items are modeled as measures of one common variable, and as only this one variable enters the causal relationship – high correlations may even improve the robustness of the applied measurement and/or structural model (Rigdon 1998: 254–255).
- 4.
The distinctive characteristics of reflective and formative measurement models will be presented in Sect. 3.2.2.
- 5.
The estimates of imperfections in the parameters of the measurement model give important information about the reliability and validity of the measurement model, which is an important pre-condition to derive reliable and valid insights from the theoretical substance of the relationship between the latent variables (Hildebrandt 2004: 545; Rigdon 1998: 254).
- 6.
- 7.
The growing popularity of PLS path modeling is reflected by its increased utilization in recent journal publications (Henseler et al. 2009: 282).
- 8.
The term “covariance” is used here in a broader sense, including both variance and correlation.
- 9.
PLS is described as a variance analytic approach (Backhaus et al. 2008: 515).
- 10.
- 11.
The limited consistency of the parameter estimates in PLS is due to the fact that a consistent approximation of the correct parameter value requires a large sample and numerous indicators for each latent construct (consistency at large) (Albers and Hildebrandt 2006: 15; Bliemel et al. 2005: 11; Chin 1998b: 329–330). Therefore, while PLS is coherent in a predictive sense (Chin 1998b: 303), its parameter estimation process – in contrast to LISREL – is not consistent (Scholderer and Balderjahn 2005: 92).
- 12.
Cf. Sect. 2.4.1.
- 13.
The distinctive characteristics of reflective and formative measurement models will be presented in Sect. 3.2.2.
- 14.
- 15.
Cf. Sect. 4.1.1.
- 16.
- 17.
- 18.
Despite not being relevant for this work, it should be noted that – apart from moderating variables – mediating variables may also influence this relationship (Shrout and Bolger 2002: 422). In the case of such mediation variables, the impact of an exogenous variable on a dependent, endogenous variable is partly or completely mediated by a so-called mediator (Eggert et al. 2005: 103). The existence of mediation effects thus leads to a partial or complete disconnection of the relationship between the exogenous constructs and the endogenous variables (Eggert et al. 2005: 103–104). Instead of the disconnection of this relationship, only effects on its strength are assumed in this work, which are better conceptualized by moderating variables (Baron and Kenny 1986: 1174; Eggert et al. 2005: 103–104). In Sect. 4.1.3, we will explain the moderating effects on the strength of this relationship in more detail.
- 19.
Latent interaction variables do not conform to this assumption, as their indicators result from multiplication with an exogenous variable, and thus inevitably share a part of their variance with the indicators of the exogenous construct (Eggert et al. 2005).
- 20.
In Sect. 3.2.2., the distinctive characteristics of reflective and formative measurement models will be presented.
- 21.
Even though formative indicators are usually slightly positively or negatively correlated, it is possible that formative indicators are highly correlated with each other, which leads to the problem of multicollinearity (Krafft et al. 2005: 78). Appropriate quality criteria to control for this problem will be presented in Sect. 3.2.3.
- 22.
The academic journals of their study included the Journal of Consumer Research, the Journal of Marketing, the Journal of Marketing Research, and Marketing Science (Jarvis et al. 2003: 206).
- 23.
The nomological aspects of indicators may differ in the case of formative measurement models (i.e., they are not required to have the same antecedents and consequences) (Jarvis et al. 2003: 203). Therefore, in contrast to reflective measurement models (i.e., where indicators have the same antecedents and consequences), the elimination of an indicator in a formative measurement model requires a check, if the new model version functions in predictable ways (Diamantopoulos and Winklhofer 2001: 273; Jarvis et al. 2003: 203).
- 24.
His analysis covered the following German academic publications: Zeitschrift für Betriebswirtschaft, Die Betriebswirtschaft, and Zeitschrift für betriebswirtschaftliche Forschung (Fassott 2006: 74).
- 25.
Cf. Sect. 4.1.
- 26.
The terms reliability and validity will be explained in more detail in the next chapter.
- 27.
First-generation quality criteria (e.g., explorative factor analysis, Cronbach’s alpha) were originally developed in the 1950s in the area of psychology/psychometrics and have been promoted mainly by the work of Churchill (1979) in marketing research (Homburg and Giering 1996: 8). With the introduction and spread of the confirmatory factor analysis in marketing research, increasingly new and more powerful quality criteria (e.g., indicator reliability, construct reliability) were developed – which were termed second-generation quality criteria (Homburg and Giering 1996: 8, 13).
- 28.
For a detailed description of explorative factor analysis cf. Hüttner and Schwarting (1999).
- 29.
The scales of the questionnaire applied in our survey have been developed for the purpose of this work and have not been utilized before (cf. Sect. 5.2.2).
- 30.
- 31.
The reasoning for avoiding the elimination of indicators in formative measurement models has been explained in Sect. 3.2.2.2.
- 32.
Cf. Sect. 3.2.3.1.
- 33.
The correlation coefficient is calculated by dividing the covariance of two metric formative indicators by the product of their standard deviations (Schulze 1998: 128).
- 34.
The external or nomological validity has been introduced to evaluate formative measurement models, as individual item reliability and convergent validity of reflective measurement models are irrelevant here, given that the latent variable is modeled as an effect instead of a cause of the manifest indicator variables (Götz and Liehr-Gobbers 2004: 729; Hulland 1999: 201).
- 35.
The MIMIC model allows a single latent variable to be measured by both formative and reflective indicators (Krafft et al. 2005: 80). As the MIMIC model is currently not supported by all PLS techniques (e.g., SmartPLS), a two-construct model is often applied to assess the measurement errors (Diamantopoulos and Winklhofer 2001: 272–273; Götz and Liehr-Gobbers 2004: 720). Here, for the external validation of the formative measurement model, an additional reflective measurement model (phantom model) is designed to specify a phantom variable (Götz and Liehr-Gobbers 2004: 720; Rindskopf 1984: 38). External validity is confirmed if a strong and significant relationship exists between the formatively operationalized latent construct and the reflectively measured, latent phantom variable (Krafft et al. 2005: 82; Rindskopf 1984: 38). If, however, no reflective indicators are available to specify the latent phantom variable, nomological validity may be assessed alternatively (Diamantopoulos and Winklhofer 2001: 273; Eggert and Fassott 2005: 41; Götz and Liehr-Gobbers 2004: 730). No reflective indicator variables were added in the survey of this work – that would correspond to the formatively measured, latent constructs – to achieve a sufficient response rate based on a minimum amount of questions (cf. Sect. 5.2.2).
- 36.
The less restrictive assumptions of PLS versus the covariance-based approach LISREL have been explained in Sect. 3.1. It should be noted here that even though a parametric approach – which recognizes the classical assumptions, particularly regarding the distribution of residuals – would allow an estimation of the standard errors of the parameters, this does not correspond to the PLS philosophy of soft modeling (Balderjahn 1986: 147; Chin 1998b: 315; Chin and Newsted 1999: 324; Lohmöller 1989: 64), and thus will not be considered in this work.
- 37.
In Sect. 4.1, the hypotheses of this work will be presented and explained in detail.
- 38.
Cf. Sect. 3.2.3.1.
- 39.
In the literature, this measure of the effect size of the interaction term is usually termed solely “effect size” (Chin et al. 2003: 195–196; Eggert et al. 2005: 109). To distinguish this measure of the effect size of interaction variables from the effect size of the exogenous variables in the basic structural model, we utilize the term “interaction effect size”.
- 40.
- 41.
A reflective relationship between the dimensions and the second-order construct would imply that the dimensions are interchangeable measures of the second-order construct, and thus are not inseparable – calling into question the necessity of a second-order construct (Albers and Götz 2006: 672–673; Maloney 2007: 258–259).
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Heinecke, P. (2011). Structural Equation Methodology. In: Success Factors of Regional Strategies for Multinational Corporations. Contributions to Management Science. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2640-1_3
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