Chapter 8: Modeling Heterogeneous Data

Learning Outcomes

  1. Comprehend the usefulness of a PLS-SEM importance–performance map analysis (IPMA).
  2. Learn how to analyze necessity statements in a PLS-SEM context.
  3. Understand higher-order constructs and how to apply this concept in PLS-SEM.
  4. Evaluate the mode of measurement model with confirmatory tetrad analysis in PLS-SEM (CTA-PLS).
  5. Grasp the concept of endogeneity and its treatment when applying PLS-SEM.
  6. Understand multigroup analysis in PLS-SEM.
  7. Learn techniques to identify and treat unobserved heterogeneity.
  8. Understand measurement model invariance and its assessment in PLS-SEM.
  9. Become familiar with consistent PLS-SEM (PLSc-SEM).

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This primer focuses on PLS-SEM’s foundations. With the knowledge gained from Chapters 1–7, researchers have the understanding for using more advanced techniques that complement the basic PLS-SEM analyses (also see Table 1 in Ghasemy, Teeroovengadum, Becker, & Ringle, 2021). Moreover, while Chapter 7 introduced the broadly applied mediator and moderator analysis techniques, this chapter provides a brief overview of some other useful and less frequently used advanced methods.


The first topic, the importance–performance map analysis (IPMA), represents a particularly valuable tool to extend the results presentation of the standard PLS-SEM estimations by contrasting the total effects of the latent variables on a specific target variable with their latent variable scores. The graphical representation of outcomes enables researchers to easily identify critical areas of attention and action. The second topic addresses recent methodological research that has  extended the PLS-SEM method to accommodate a sufficiency logic in which an antecedent construct may be sufficient to produce a certain outcome but may not be necessary. Specifically, researchers have jointly used PLS-SEM and necessary condition analysis to derive a nonlinear ceiling function, which facilitates disclosing the minimum level of an antecedent construct required to obtain a certain level of the endogenous construct. The third topic introduces higher-order constructs that measure concepts on different levels of abstraction in a PLS path model. From a conceptual perspective, using higher-order constructs is often more appropriate than relying on standard one-dimensional constructs. Their application typically facilitates reducing the number of structural model relationships, making the PLS path model more parsimonious and easier to grasp. The fourth topic covered is confirmatory tetrad analysis—a useful tool to empirically substantiate the mode of a latent variable’s measurement model (i.e., formative or reflective). The application of confirmatory tetrad analysis enables researchers to avoid incorrect measurement model specifications. The fifth topic that has raised considerable research interest is endogeneity, which occurs when a predictor construct is correlated with the error term of the dependent construct to which it is related. Endogeneity is of particular concern for explanatory analyses as it may entail biased parameter estimates and trigger type I and type II errors. Researchers have proposed various approaches for identifying and treating endogeneity, which can be generalized to a PLS-SEM context. The sixth topic summarizes ways to deal with heterogeneity in the data. We first discuss multigroup analysis, which enables testing for significant differences among path coefficients, typically between two groups. Moreover, we deal with unobserved heterogeneity, which if neglected is a threat to the validity of PLS-SEM results. We also introduce standard as well as more recently proposed latent class techniques and make recommendations regarding their use. Comparisons of PLS-SEM results across different groups are only reasonable if measurement invariance is confirmed. For this purpose, the measurement invariance of composites procedure provides a useful tool in PLS-SEM. Finally, we provide an overview of consistent PLS-SEM, which applies a correction for attenuation to PLS path coefficients. When applied, PLS path models with reflectively measured latent variables estimate results that are the same as CB-SEM, while retaining some of the well-known advantages of PLS-SEM. We discuss most topics in greater detail in our book Advanced Issues in Partial Least Squares Structural Equation Modeling (Hair, Sarstedt, Ringle, & Gudergan, 2018). Also, the article on structural robustness checks in PLS-SEM by Sarstedt, Ringle et al. (2020) further highlights some of the topics discussed in this chapter.