Estimating models with independent observed variables based on the PLSe2 methodology: a Monte Carlo simulation study

There are two versions of efficient partial least squares (PLSe) methodology, PLSe1 and PLSe2. PLSe2 utilizes the generalized least squares (GLS) covariance structure estimation methodology, and its performance has been verified under different normality and non-normality conditions. Based on this methodology, there must be no independent observed variables in the model. However, there are many instances where researchers would like to estimate models which contain independent observed variables. To address this issue, we propose the methodology of representing the independent observed variables with dummy factors. We take two model-implied covariance matrices from two studies on a nonstandard model and a simple mediation model, use them to generate random samples for our simulations under normality and non-normality conditions, and validate the proposed methodology. We also compare our results across PLSe2 and maximum likelihood (ML) and provide evidence for the estimates’ statistical properties being maintained when artificial variables (i.e., dummy factors) are included in the model. Our results show that while the proposed methodology works well due to the comparability of the estimates and the root mean square error (RMSE) statistics across PLSe2 and ML, the Satorra–Bentler methodology should be considered when PLSe2 is used to estimate models involving dummy factors using both multivariate normal and non-normal data. Last, we provide an illustrative application to demonstrate our simple, practical, and remedial approach in EQS.