Second Order Model with Composite Quantile Regression

Abstract

In many fields, comprehensive evaluation is a very important topic. Both second order model and its modified one with quantile regression have been widely used in evaluation. Although quantile-type second order model has abilities in capturing a complete picture of different variables’ relations at different quantile levels. Sometimes we find it complex to summarize the conclusions of all quantile levels. Therefore, we propose a new second order model with composite quantile regression, which has the advantage of obtaining a whole evaluation result based on all quantile levels. More specifically, one of our paper’s main contributions is to develop a comprehensive evaluation model based on the classical second order model, quantile regression and composite quantile regression. What’s more, we introduce a modified partial least square estimation algorithm under the well-known partial least squares framework. The new algorithm has the ability in estimating both path and loading coefficients reflecting the relationships among manifest variables and latent variables at all quantile levels.