Structural equation modeling (SEM) is a system of two kinds of equations: a linear latent structural model (SM) and a linear measurement model (MM). The latent structure model is a causal model from the latent parent node to the latent child node. Meanwhile, MM’s link is from latent variable parent node to observed variable child node. However, researchers should determine the initial causal order between variables based on experience when applying SEM. The main reason is that SEM does not fully construct causal models between observed variables (OVs) from big data. When the artificial causal order is contrary to the fact, the causal inference from SEM is doubtful, and the implicit causal information between the OVs cannot be extracted and utilized. This study first objectively identifies the causal order of variables using the DirectLiNGAM method widely accepted in recent years. Then traditional SEM is converted to expanded SEM (ESEM) consisting of SM, MM and observation model (OM). Finally, through model testing and debugging, ESEM with good fit with data is obtained.
Analysis of approximations of GUM supplement 2 based non-Gaussian PDFs of measurement models with Rosenblatt Gaussian transformation mappings