A class of new partial least square algorithms for first and higher order models

Abstract

We propose a class of new partial least square (PLS) algorithms to build first and higher order latent variable models. There exist three well-known linear-regression-type PLS algorithms: Repeated indicators approach (RI), two-step approach (TS), and hybrid approach (H). RI uses observed variables repeatedly and leads to a possible bias of the estimates. TS needs two separate steps and does not take higher order latent variables into account when computing the scores of lower order constructs at the first step. H randomly assigns all observed variables to latent variables and may lead to the uncertainty of structure relationship each time. In addition, all the above linear-regression-type PLS algorithms only offer a conditional mean view of the relationships among variables and thus fail in quantifying the relationships at different levels. The new PLS algorithms use quantile regression to broaden this view by allowing coefficients to be estimated at different quantiles. Because of this attractive feature, we can capture overall view of structure relationships and complex associations among variables and highlight the changing relationships according to the explored quantile of interest. Our new PLS algorithms are compared to the existing ones in simulation studies, and applied to part of the 2018 Global Innovation Index study.

Keywords:

• Latent variable model
• Partial least square
• Quantile regression

Acknowledgments

The author is very grateful to the reviewers and editors for their many helpful comments and suggestions that have led to better presentation and improvements in the paper. The author gratefully acknowledges The Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (16XNH102). In addition, The author wants to thank his parents' support since he was born and his wife Yujie Liu's patience, care and love. "To the world you may be one person, but to me you are the world.”