Revisiting and Extending PLS for Ordinal Measurement and Prediction

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.