New Partial Least Square Third-order Latent Variable Models

Abstract

As a special case of higher-order model, third-order model has the abilities to reflect the relations among more different levels of indicators. More specially, third-order here means that there exist three different orders of latent variables and certain amounts of observed variables. The main challenge for third-order model lies in the estimation of unknown path and loading coefficients due to the complex structure inside. Our paper proposes a new estimation algorithm for third-order model under the framework of partial least square. On the above basis, we further develop a new partial least square third-order model with quantile regression and propose a new modified algorithm correspondingly. This kind of model can capture the relations among different variables at different quantiles. In addition, we develop another new partial least square third-order model with varying coefficients, which reflecting the dynamic relations among different latent variables and observed variables.