A Penalized Likelihood Method for Structural Equation Modeling and Its Extensions

Abstract

Structural equation modeling (SEM) is a commonly used multivariate statistical method in psychological studies. Under SEM framework, researchers can flexibly specify their models based on available psychological theories and test the plausibility of the hypothesized models. In this talk, a penalized likelihood (PL) method for SEM is introduced. Compared to the usual likelihood, PL includes a penalty term to control the complexity of the hypothesized model. When the penalty level is chosen appropriately, PL can yield a model that balances 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. An R package lsl can be used to implement the ECM algorithm. Theorems on the asymptotic behaviors of PL are derived. Simulations are conducted to evaluate the empirical performance of the proposed PL method. Finally, several extensions of PL under SEM framework will be also introduced, including SEM with missing data, ordinal data SEM, and multi-group SEM.