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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.
Acknowledgements
The first author (she) wishes to thank the Scientific and Technological Research Council of Turkey (TUBITAK) for their support and Professor Bozdogan for his supervision of her research project which culminated in this paper as a Post Doctoral Research Fellow under him. The authors also express their gratitude to Dr. J. Andrew Howe for his computational assistance during this research and two anonymous reviewers of the manuscript. Their comments and careful reading improved the paper further.