Regularizing Structural Equation Models via the Lasso : Generalizability and Reproducibility Issues

Abstract

Generalizability and Reproducibility of research have become one of the main topics in current psychology. Previous discussions on the issue have focused on the Experimental/Procedural aspect such as incentive structure for researchers, violation in conducting an experiment, selective reporting, etc. However, sometimes statistical methods which are widely used in psychology have properties that undermine the generalizabilty of research results. The present thesis approaches the reproducibility problem based on this Analytical/Statistical aspect. For this purpose, we studied a method for improving the Structural Equation Modeling(SEM), one of dominant statistical models in psychology. The main focus of this study is implementing L1-regularization, or Lasso, to SEM. With this method, the result will enjoy less variability of estimation than the existing Maximum Likelihood method. First of all, the present thesis discusses some indices including Overall Discrepancy(OD) and Mean Squared Error(MSE) as criteria which indicate the generalizability and reproducibility of analysis results. Bayesian Lasso SEM, one of the previous attempts, is also covered with some fundamental issues. Furthermore, an algorithm for regularizing SEM via the Lasso is derived and examined by several simulation studies. The study is carried out using Factor Analysis Model and Structural Equation Modeling, while adding several misspecified parameters. The purpose of this approach is to test Lasso SEMs complete shrinkage ability, which is able to detect and remove unnecessary parameters from the original model so that the method yields the result close to the true population-generating process. It is also investigated whether Lasso can improve generalizability and reproducibility by observing and comparing OD and MSE. The simulation deals with various conditions including model error, sample sizes, and magnitudes of covariance matrix, in order to examine in which condition Lasso SEM yields better results than the Maximum Likelihood Estimation. The result reveals that Lasso SEM works well in various conditions

it improves generalizability indices, detects and removes misspecified parameters in the original model. However, the performance depends on the conditions, which implies that the Lasso SEM should be applied with careful scrutiny on characteristics of practical data. Especially, the model error, one of the component affecting the data-generating process, has turned out to be the most influential factor that hinders proper function of the Lasso SEM. We suggest modifying the optimization of Lasso SEM, which is currently rely upon the value of OD, or its cross-validation estimate. The improvement can be achieved by replacing criteria or objective function in the optimization procedure. This will minimize problems including those generated from the model error. A correlation analysis shows that Sample Discrepancy, which is a criterion of the existing estimation method, and goodness of model fit indices widely used in SEM have considerably low correlations with OD. This outcome implies the SEM result obtained by the original method may be hard to be generalized to other independent samples including the future data, and the phenomenon that researchers are interested in.