Data Smoothing Structural Equation Modeling to Study Quality of Life and Model Selection

Abstract

In this paper, we propose and present a nonparametric data smoothing method via the kernel smoothing functions to make structural equation modeling (SEM) robust to a specific type of model misspecification, that is an incorrect distributional assumption. Although most statistical techniques are based on an implicit assumption of normality, real data often exhibits nonnormal kurtosis (heavily peaked), skewness, or both. These characteristics, if ignored, can make model identification difficult and inference not reliable. It is important to note that these are characteristics present in most real multivariate high-dimensional datasets. There is much recent study devoted to this type of misspecification. Using a large scale Monte Carlo simulation study, we evaluate the efficacy of our proposed approach in improving the frequency with which a correctly specified model is selected by information complexity criteria when the normality is misspecified. We also show our results on a benchmark reference real dataset to study the quality of life. Our results indicate that the data smoothing kernel transformation (KDS-SEM) leads to a better fitting structural equation model (SEM) and model selection.