B-spline estimation algorithms in quantile-based dynamic structural equation models

In many applications, the structural equation models with varying coefficients and changing quantiles are urgently needed. The estimation of the varying coefficients at different quantile levels brings difficulties and challenges especially in complex structural relations. In our article, we propose two kinds of quantile-based dynamic structural equation models: a quantile-based structural equation model with varying coefficients and a composite-quantile-based structural equation model with varying coefficients. Based on the above two new models, the paper first proposes a B-spline estimation algorithm based on the quantile regression estimation and then develops its extension algorithm based on the composite quantile regression estimation. The former algorithm allows the varying coefficients to be estimated at different quantiles, and the latter one simultaneously considers multiple quantile levels. A set of simulation studies is carried out to investigate the performances of our proposed algorithms and the paper finally applies the proposed models and algorithms to a real data example.