A Penalized Likelihood Method for Structural Equation Modeling and Its Asymptotic Properties

• Main Authors: Po-Hsien Huang, 黃柏僩
• Other Authors: Li-Jen Weng
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/23330647061588147692

博士 === 國立臺灣大學 === 心理學研究所 === 102 === Structural equation modeling (SEM) is a commonly used multivariate statistical method in psychological studies. The application of SEM involves a confirmatory testing of the models proposed by researchers based on available theories. Yet, in practice, a model generating approach, where modifications of the models are being explored, may well take place (Joreskog, 1993), especially when the development of the substantive theory is still in its infancy. A method for SEM that can embrace the existing theories on one hand and the ambiguous relations that await further exploration on the other will be of great value to advancing scientific theories. In this dissertation, a penalized likelihood (PL) method for SEM is proposed as an attempt to target this goal. Under the proposed PL method, an SEM model is formulated with a confirmatory part and an exploratory part. The confirmatory part contains all the theory-derived relations and constraints. The exploratory part, wherein a set of penalized parameters is specified to represent the ambiguous relations, is data-driven yet with model complexity controlled by the penalty term. Through the sparse estimation of PL, the relationships among variables can be efficiently explored. As the penalty level is chosen appropriately, PL can lead to a SEM model that balances the tradeoff between model goodness-of-fit and model complexity. An expectation-conditional maximization (ECM) algorithm is developed to maximize the PL estimation criterion with several state-of-art penalty functions. Four theorems on the asymptotic behaviors of PL are derived, including the local and global oracle property of PL estimators and the selection consistency of Akaike and Bayesian information criterion. Two simulations are conducted to evaluate the empirical performance of the proposed PL method, and finally the practical utility of PL is demonstrated using two real data examples.