A penalized likelihood method for multi-group structural equation modelling.

In the past two decades, statistical modelling with sparsity has become an active research topic in the fields of statistics and machine learning. Recently, Huang, Chen and Weng (2017, Psychometrika, 82, 329) and Jacobucci, Grimm, and McArdle (2016, Structural Equation Modeling: A Multidisciplinary Journal, 23, 555) both proposed sparse estimation methods for structural equation modelling (SEM). These methods, however, are restricted to performing single-group analysis. The aim of the present work is to establish a penalized likelihood (PL) method for multi-group SEM. Our proposed method decomposes each group model parameter into a common reference component and a group-specific increment component. By penalizing the increment components, the heterogeneity of parameter values across the population can be explored since the null group-specific effects are expected to diminish. We developed an expectation-conditional maximization algorithm to optimize the PL criteria. A numerical experiment and a real data example are presented to demonstrate the potential utility of the proposed method.