Revisiting and Extending PLS for Ordinal Measurement and Prediction

Traditionally, partial least squares (PLS) and consistent partial least squares (PLSc)Partial Least Squares (PLS)consistent PLS (PLSc) assume the indicators to be continuous. To relax this restrictive assumption, ordinal partial least squares (OrdPLS)OrdinalPLS (OrdPLS) and ordinal consistent partial leastPartial Least Squares (PLS)ordinal consistent PLS (OrdPLSc) squaresOrdinalconsistent PLS (OrdPLSc) have been developed. They are extensions of PLS and PLScPartial Least Squares (PLS)consistent PLS (PLSc), respectively, that are able to take into account the nature of ordinal variables—both belonging to exogenousExogenous and endogenousEndogenous constructs. In the PLS context, assessing the out-of-sample predictive power of models has increasingly gained interest. In contrast to PLS and PLScPartial Least Squares (PLS)consistent PLS (PLSc), performing out-of-sample Predictionout-of-sample prediction predictionsOut-of-sample predictions is not a straightforward process for OrdPLSOrdinalPLS (OrdPLS) and OrdPLSc Ordinalconsistent PLS (OrdPLSc) becausePartial Least Squares (PLS)ordinal consistent PLS (OrdPLSc) the two assume that ordinal indicators are the outcome of categorized unobserved continuous variables, i.e., they rely on polychoricPolychoric and polyserialPolyserial correlations correlationsCorrelationpolyserial. In this chapter, we present OrdPLSpredict and OrdPLScpredict to perform out-of-sample Predictionout-of-sample prediction predictionsOut-of-sample predictions with models estimated by OrdPLSOrdinalPLS (OrdPLS) and Partial Least Squares (PLS)ordinal consistent PLS (OrdPLSc) OrdPLScOrdinalconsistent PLS (OrdPLSc). A Monte Carlo simulationMonte Carlosimulation demonstrates the performance of our proposed approach. Finally, we provide concise guidelines using the open source R package cSEMCSEM to enable researchers to apply OrdPLSpredict and OrdPLScpredict using an empirical example.