Chapter 8: Modeling Heterogeneous Data

Learning Outcomes

  1. Comprehend the usefulness of a PLS-SEM importance-performance map analysis (IPMA).
  2. Understand hierarchical component models (HCMs) and how to apply this concept in PLS-SEM.
  3. Get to know how to assess the mode of measurement model with the confirmatory tetrad analysis in PLS-SEM (CTA-PLS).
  4. Understand multigroup analysis in PLS-SEM.
  5. Learn about techniques to identify and treat unobserved heterogeneity.
  6. Understand measurement model invariance and its assessment in PLS-SEM.
  7. Become familiar with consistent partial least squares (PLSc).

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This primer focuses on PLS-SEM’s foundations. With the knowledge gained from Chapters 1 to 6, researchers have the understanding for using more advanced techniques that complement the basic PLS-SEM analyses. While Chapter 7 introduced the broadly applied mediator and moderator analysis techniques, this chapter offers a brief overview of some other useful and less frequently used advanced methods. To start with, the importance-performance map analysis 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 some target variable with their latent variable scores. The graphical representation of outcomes enables researchers to easily identify critical areas of attention and action. The next topic focuses on hierarchical component models, which enable researchers to represent constructs measured on different levels of abstraction in a PLS path model. From a conceptual perspective, using hierarchical component models is often more appropriate than relying on standard one-dimensional constructs. Their use typically allows reducing the number of structural model relationships, making the PLS path model more parsimonious and easier to grasp. The method that follows, confirmatory tetrad analysis, is 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 specification. The following sections address ways of dealing with heterogeneity in the data. We first discuss multigroup analysis, which enables testing for significant differences among path coefficients, typically between two groups. We also 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 composite procedure provides a useful tool in PLS-SEM. Finally, we introduce consistent PLS, 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 many of the well-known advantages of PLS-SEM.