Latent Structure Linear Regression


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.

Share and Cite:

Höskuldsson, A. (2014) Latent Structure Linear Regression. Applied Mathematics, 5, 808-823. doi: 10.4236/am.2014.55077.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Hoskuldsson, A. (1996) Prediction Methods in Science and Technology. Vol. 1, Thor Publishing, Copenhagen.
[2] Hoskuldsson, A. (2009) Modelling Procedures for Directed Network of Data Blocks. Chemometrics and Intelligent Laboratory Systems, 97, 3-10.
[3] Hoskuldsson, A. (2008) H-Methods in Applied Sciences. Journal of Chemometrics, 22, 150-177.
[4] Hoskuldsson, A. (1994) Data Analysis, Matrix Decompositions and Generalised Inverse. SIAM Journal on Scientific Computing, 15, 239-262.
[5] Clinical and Laboratory Standards Institute.
[6] Kennard, R.W. and Stone, L.A. (1969) Computer Aided Design of Experiment. Technometrics, 11, 43-64.
[7] Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985) Modern Multivariate Analysis: A Graduate Course and Handbook. American Science Press, Columbus.
[8] Roger, J.M., Palagos, B., Bertrand, D. and Fernandez-Ahumada, E. (2011) CovSel: Variable Selection for Highly Multivariate and Multi-Response Calibration. Application to IR Spectroscopy. Chemometrics and Intelligent Laboratory Systems, 106, 216-223.
[9] Hoskuldsson, A. (2001) Variable and Subset Selection in PLS Regression. Chemometrics and Intelligent Laboratory Systems, 557, 23-38.
[10] Reinikainen, S.-P. and Hoskuldsson, A. (2003) COVPROC Method: Strategy in Modeling Dynamic Systems. Journal of Chemometrics, 17, 130-139.
[11] Grove, H., et al. (2008) Combination of Statistical Approaches for Analysis of 2-DE Data Gives Complementary Results. Proteome Research, 7, 5119-5124.
[12] McLeod, G., et al. (2009) A Comparison of Variate Pre-Selection Methods for Use in Partial Least Squares Regression: A Case Study on NIR Spectroscopy Applied to Monitoring Beer Fermentation. Journal of Food Engineering, 90, 300-307.
[13] Tapp, H.S., et al. (2012) Evaluation of Multiple Variate Methods from a Biological Perspective: A Nutrigenomics Case Study. Genes & Nutrition, 7, 387-397.
[14] Bruker Optics, Germany.
[15] Micro-Biolytics, Germany.
[16] Perez-Guaita, D. et al. (2013) Modified Locally Weighted—Partial Least Squares Regression, Improving Clinical Predictions from Infrared Spectra of Human Serum Samples. Talanta, 170, 368-375.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.