Parametric and Non Parametric Approach in Structural Equation Modeling (SEM): The Application of Bootstrapping

Lately, there was some attention for the Variance Based SEM (VB-SEM) against that of Covariance Based SEM (CB-SEM) from social science researches regarding the fitness indexes, sample size requirement, and normality assumption. Not many of them aware that VB-SEM is developed based on the non-parametric approach compared to the parametric approach of CB-SEM. In fact the fitness of a model should not be taken lightly since it reflects the behavior of data in relation to the proposed model for the study. Furthermore, the adequacy of sample size and the normality of data is among the main assumptions of parametric test itself. This study intended to clarify the ambiguities among the social science community by employing the data-set which do not meet the fitness requirements and normality assumptions to execute both CB-SEM and VB-SEM. The findings reveal that the result of CB-SEM with bootstrapping is almost similar to that of VB-SEM (bootstrapping as usual). Therefore, the failure to meet the fitness and normality requirements should not be the reason for employing Non-Parametric SEM.