TITLE:
Latent Structure Linear Regression
AUTHORS:
Agnar Höskuldsson
KEYWORDS:
H-Principle of Mathematical Modelling; H-Methods; PLS Regression; Latent Structure Regression
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.5,
March
24,
2014
ABSTRACT:
A short review is given of standard regression
analysis. It is shown that the results presented by program packages are not
always reliable. Here is presented a general framework for linear regression
that includes most linear regression methods based on linear algebra. The
H-principle of mathematical modelling is presented. It uses the analogy between
the modelling task and measurement situation in quantum mechanics. The
principle states that the modelling task should be carried out in steps where
at each step an optimal balance should be determined between the value of the
objective function, the fit, and the associated precision. H-methods are
different methods to carry out the modelling task based on recommendations of
the H-principle. They have been applied to different types of data. In general,
they provide better predictions than linear regression methods in the
literature.