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.

中文翻译：

---

多组结构方程建模的惩罚似然法。

在过去的二十年中，具有稀疏性的统计建模已成为统计和机器学习领域的活跃研究主题。最近，Huang，Chen和Weng（2017，Psychometrika， 82，329）和Jacobucci，Grimm和McArdle（2016，结构方程建模：多学科期刊，23（555）都提出了用于结构方程模型（SEM）的稀疏估计方法。但是，这些方法仅限于执行单组分析。本工作的目的是为多组SEM建立一种惩罚似然（PL）方法。我们提出的方法将每个组模型参数分解为一个公共参考分量和一个特定于组的增量分量。通过惩罚增量分量，可以探索整个种群中参数值的异质性，因为预期空组特定的影响将减少。我们开发了期望条件最大化算法来优化PL标准。数值实验和实际数据例子说明了该方法的潜在实用性。