Quantile-based structural equation models with their applications in CGSS data

Quantile-based structural equation models are urgently needed in various applications and fields due to their distinct features in capturing relations among different variables at the explored quantile of interest. The article proposes composite quantile-based structural equation model (CQ-SEM) and a class of estimation algorithms under the framework of partial least squares. More specifically, these proposed algorithms are developed based on the existing alternating direction method of multipliers, interior point, and majorize-minimization in composite quantile regression. The CQ-SEM model and algorithms allow the relations among different variables to be captured simultaneously at multiple quantile levels. The CQ-SEM model and its corresponding algorithms are compared to existing classical and quantile-based structural equation models in the simulation studies and applied to Chinese child and adolescent online health investigations based on part of Chinese General Social Survey data.