We deal with a model selection problem for structural equation modeling (SEM) with latent variables for diffusion processes. Based on the asymptotic expansion of the marginal quasi-log likelihood, we propose two types of quasi-Bayesian information criteria of the SEM. It is shown that the information criteria have model selection consistency. Furthermore, we examine the finite-sample performance of the proposed information criteria by numerical experiments.

翻译：本文研究具有潜变量的扩散过程结构方程模型(SEM)的模型选择问题。基于边际拟对数似然的渐近展开，我们提出了两种类型的SEM准贝叶斯信息准则。研究证明这些信息准则具有模型选择一致性。此外，我们通过数值实验检验了所提出信息准则在有限样本下的性能表现。