Robust Partial Least Squares Structural Equation Modeling With Mode A

As a method to estimate the relationships among latent(unobservable)variables as well as those of the manifest(observable)variables,partial least squares SEM(PLS-SEM)is often used when the model becomes complicated while theoretical knowledge is scarce.Data in social sciences are typically nonnormally distributed and characterized by heavy tails.However,outliers or heavy-tailed distributions can seriously distort the results of statistical analyses and thus threaten the validity of statistical methods.Like least squares(LS),PLS-SEM is highly sensitive to outliers.Although PLS-SEM theories have been extended and advanced over the past several decades,few studies have focused on improving the PLS-SEM methods when outliers exist.There are two different modes--Mode A and Mode B--in PLS-SEM in estimating the weights for computing the proxies to latent variables.Principal component analysis(PCA)and canonical correlation analysis(CCA)are two special cases of the two modes.Combined with robust regression and Mode A,this thesis proposes a robust partial least squares SEM(RPLS-SEM)method to counter the effects of outliers.Main works of this thesis are as follows:1.RPLS-SEM is proposed with using the slope of robust regression to estimate PLS weight and downweighting the effect of outliers to estimate the scores of latent variables.2.Based on the RPLS-SEM method,robust partial least squares PCA(RPLS-PCA)is developed to robustly estimate eigenvalues,eigenvectors and principal component scores.3.Monte Carlo simulations are used to evaluate the performance of the proposed RPLS-SEM method by comparing it against the conventional PLS-SEM and another method of robust transformation.The results show that the RPLS-SEM method can provide more reliable parameter estimates for PCA and structural equation modeling(SEM)under most conditions.4.Through a practical PCA example,the differences of the above three methods in applications are compared.