Quantile varying-coefficient structural equation model

In the article, we develop a quantile varying-coefficient structural equation model in which the coefficients are allowed to vary as smooth functions of other variable at different quantiles. A new local-polynomial-based (LP) estimation method is proposed for estimating the model flexibly. A class of estimated loading coefficients and path coefficients is obtained to capture the dynamic relations among latent variables and observed variables at different quantiles. In addition, the distinct advantages of the proposed LP estimation method consists of making minimal assumptions on the distribution of data and enabling to calculate the values of latent variables. Simulation studies are carried out to further investigate the performances of the proposed LP estimation method. Finally, we further illustrate our proposed model and estimation method by two real data examples: Air pollution monitoring and talent flow exploring.