Consistent Estimates from Biased Estimators: Monte-Carlo Consistent Partial Least Squares for Latent Interaction Models with Ordinal Indicators

Structural equation models (SEMs) with latent interactions are widely used in psychologicalresearch, but estimation becomes challenging when indicators are ordinal.Existing PLS-based methods cannot simultaneously handle ordinal measurementand latent interactions: traditional PLS ignores the ordinal scale, whereas OrdPLScis not applicable to interaction models. We propose a general simulation-basedbias-correction procedure based on stochastic root finding and apply it to developMonte-Carlo Ordinal Consistent Partial Least Squares (MC-OrdPLSc). The methodtreats PLS as an inconsistent but informative estimator and iteratively simulatesdata from candidate parameters, matching the resulting PLS estimates to those obtainedfrom the observed data. This approach corrects both attenuation in reflectiveconstructs and bias from treating ordinal indicators as continuous. A Monte Carlostudy shows that MC-OrdPLSc yields approximately unbiased estimates of mainand interaction effects and achieves efficiency comparable to LMS-CAT, providing apractical approach for ordinal interaction models in PLS-SEM.