AI 中文总结
研究针对结构方程模型的模型选择问题，提出基于综合完全数据似然性的两个新信息准则，通过模拟研究评估性能，结果表明重要性抽样策略适用多种场景，ICL准则在准确估计潜在变量时效果好，证明利用潜在结构开发准则的益处。
AI 中文摘要
结构方程模型（SEM）广泛用于描述潜在变量之间的依赖结构，模型选择是许多应用中的关键问题。现有信息准则通常基于综合观测数据似然性，未明确考虑模型的潜在结构。本文提出两个基于综合完全数据似然性的新信息准则。第一个将综合完全似然性准则应用于高斯SEM，第二个通过纳入潜在结构信息并使用重要性抽样策略来近似综合观测数据对数似然性。通过广泛模拟研究评估其性能，结果表明重要性抽样策略在多种场景下提供稳健且有竞争力的模型选择，而ICL准则在准确估计潜在变量时对恢复潜在依赖结构特别有效。这些发现证明了在为结构方程模型开发信息准则时明确利用潜在结构的潜在益处。
英文摘要
Structural equation models (SEM) are widely used to describe dependency structures between latent variables, making model selection a key issue in many applications. Existing information criteria are generally based on the integrated observed-data likelihood and therefore do not explicitly account for the latent structure of the model. In this paper, we propose two new information criteria derived from the integrated complete-data likelihood. The first adapts the Integrated Completed Likelihood criterion to Gaussian SEM, while the second proposes an alternative approach to approximating the integrated observed-data log-likelihood by incorporating latent structural information and using an importance sampling strategy. Their performance is assessed through an extensive simulation study covering null, direct, indirect and complete latent structures under different sample sizes and signal strengths. The results show that the proposed importance sampling strategy provides robust and competitive model selection across a wide range of scenarios, whereas the proposed ICL criterion is particularly effective for recovering latent dependency structures when the latent variables are accurately estimated. These findings demonstrate the potential benefits of explicitly exploiting the latent structure when developing information criteria for structural equation models.
