Abstract

There is a growing interest among methodological and applied researchers in extending the use of regularization techniques (e.g., lasso regression, the elastic net) to structural equation models (SEMs). To date, most of the extensions have been based on combining the respective penalty function with the standard Maximum Likelihood fit function for SEMs. In the present article, we describe two ways in which the Two-Stage Least Squares (2SLS) estimator, an equation-by-equation estimator of SEMs, can be combined with these regularization techniques. Both approaches can be used to regularize the parameters in single equations (“local” regularization), and for both approaches, the parameters can be determined very quickly and efficiently using standard software. We evaluated the two methods in two simulation studies. We were able to show that both approaches provide suitable parameter estimates and can be used to select factor models and path coefficients even when the model is incorrectly specified.

摘要

方法论和应用研究人员对将正则化技术（例如，套索回归、弹性网）的使用扩展到结构方程模型 (SEM) 的兴趣日益浓厚。迄今为止，大多数扩展都是基于将相应的惩罚函数与 SEM 的标准最大似然拟合函数相结合。在本文中，我们描述了两个两阶段最小二乘 (2SLS) 估计器（SEM 的逐方程估计器）可以与这些正则化技术相结合的方法。这两种方法都可用于对单个方程中的参数进行正则化（“局部”正则化），并且对于这两种方法，都可以使用标准软件非常快速有效地确定参数。我们在两项模拟研究中评估了这两种方法。我们能够证明这两种方法都提供了合适的参数估计，并且即使在模型指定不正确的情况下也可以用于选择因子模型和路径系数。