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Revisiting and Extending PLS for Ordinal Measurement and Prediction

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Partial Least Squares Path Modeling

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Abstract

Traditionally, partial least squares (PLS) and consistent partial least squares (PLSc) assume the indicators to be continuous. To relax this restrictive assumption, ordinal partial least squares (OrdPLS) and ordinal consistent partial least squares have been developed. They are extensions of PLS and PLSc, respectively, that are able to take into account the nature of ordinal variables—both belonging to exogenous and endogenous constructs. In the PLS context, assessing the out-of-sample predictive power of models has increasingly gained interest. In contrast to PLS and PLSc, performing out-of-sample predictions is not a straightforward process for OrdPLS and OrdPLSc because the two assume that ordinal indicators are the outcome of categorized unobserved continuous variables, i.e., they rely on polychoric and polyserial correlations. In this chapter, we present OrdPLSpredict and OrdPLScpredict to perform out-of-sample predictions with models estimated by OrdPLS and OrdPLSc. A Monte Carlo simulation demonstrates the performance of our proposed approach. Finally, we provide concise guidelines using the open source R package cSEM to enable researchers to apply OrdPLSpredict and OrdPLScpredict using an empirical example.

An earlier version of this chapter was published in the following Ph.D. thesis: Schamberger T. (2022) Methodological Advances in Composite-based Structural Equation Modeling. University of Würzburg/University of Twente, https://doi.org/10.3990/1.9789036553759.

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Notes

  1. 1.

    In line with recent literature (e.g., Benitez et al., 2020; Yu et al., 2021; Schamberger et al., 2023), we use the term ‘emergent variable’ to emphasize that the variable is not only a composite, i.e., a weighted linear combination of variables, but also a composite that conveys all the information between its indicators and other variables in the model.

  2. 2.

    Note that the following subsections contain large parts adapted from Schuberth et al. (2018). Which is released under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

  3. 3.

    In empirical work two consecutive threshold parameters can be equal, \(\tau _{m-1}=\tau _m\), if the corresponding category \(x_m\) is not observed.

  4. 4.

    Note that the choice of inner weighting scheme can substantially affect the estimates in the case of models containing second-order constructs (Becker et al., 2012; Schuberth et al., 2020). For more details on the other inner weighting schemes, see Tenenhaus et al. (2005).

  5. 5.

    Here we do not consider the use of Mode B for latent variables. For a consistent version of PLS using Mode B, the interested reader is referred to Dijkstra (2011).

  6. 6.

    In cases where only values of a subset of the indicators associated with endogenous constructs are predicted, a subset of the indicators associated with the exogenous constructs might be sufficient.

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Authors and Affiliations

  1. Faculty of Engineering Technology, Department of Design, Production and Management, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands

    Tamara Schamberger & Florian Schuberth

  2. Faculty of Business Management and Economics, University of Würzburg, Sanderring 2, 97070, Würzburg, Germany

    Tamara Schamberger

  3. Faculty of Economics, Department of Statistical Science, Università Cattolica del Sacro Cuore, Largo A. Gemelli, 1, 20123, Milan, Italy

    Gabriele Cantaluppi

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  1. Tamara Schamberger
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  2. Gabriele Cantaluppi
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Correspondence to Tamara Schamberger .

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Editors and Affiliations

  1. HLC Consulting, Semarang, Indonesia

    Hengky Latan

  2. Mitchell College of Business, University of South Alabama, Mobile, AL, USA

    Joseph F. Hair, Jr.

  3. Institute of International Education, Stockholm University, Stockholm, Sweden

    Richard Noonan

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Schamberger, T., Cantaluppi, G., Schuberth, F. (2023). Revisiting and Extending PLS for Ordinal Measurement and Prediction. In: Latan, H., Hair, Jr., J.F., Noonan, R. (eds) Partial Least Squares Path Modeling. Springer, Cham. https://doi.org/10.1007/978-3-031-37772-3_6

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