Latent Structure Linear Regression: A Review

Abstract

A short review of standard regression analysis is provided. It is demonstrated that programme package findings are not always trustworthy. The majority of linear regression techniques based on linear algebra are included in the general framework for linear regression that is provided here. It presents the mathematical modelling H-principle. It makes use of the comparison between the quantum mechanical measurement situation and the modelling task. According to the guiding principle, the modelling process should be completed in stages, with each stage involving the determination of the best possible compromise between the value of the objective function, the fit, and the related precision. H-methods are different methods to carry out the modelling task based on recommendations of the H-principle. A review on author’ experience on model validation is presented. FTIR data of glucose in blood serum is used for illustration. A study of these data is carried out using PLS Regression and Ridge Regression. Very little difference is found for these two methods. However, there are properties of Ridge Regression that are not attractive. It is illustrated that latent structure regression uses much lower dimension than alternative methods.