🤖 AI Summary
This study addresses the limitation of existing information criteria in structural equation modeling, which fail to explicitly leverage latent variable structures, thereby constraining model selection performance. To overcome this, the authors propose two novel information criteria based on the complete-data likelihood, uniquely integrating complete-data likelihood with importance sampling to explicitly incorporate latent variable structure into criterion design. Within the Gaussian structural equation modeling framework, the approach accurately estimates latent variables, thereby effectively recovering dependencies among observed variables. Empirical evaluations demonstrate that the proposed criteria exhibit robust performance across diverse latent structures and sample conditions, significantly outperforming existing methods—particularly when latent variable estimation is accurate.
📝 Abstract
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.