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
Cite this paper
Höskuldsson, A. (2014) Latent Structure Linear Regression. Applied Mathematics
, 808-823. doi: 10.4236/am.2014.55077
 Hoskuldsson, A. (1996) Prediction Methods in Science and Technology. Vol. 1, Thor Publishing, Copenhagen.
 Hoskuldsson, A. (2009) Modelling Procedures for Directed Network of Data Blocks. Chemometrics and Intelligent Laboratory Systems, 97, 3-10. http://dx.doi.org/10.1016/j.chemolab.2008.09.002
 Hoskuldsson, A. (2008) H-Methods in Applied Sciences. Journal of Chemometrics, 22, 150-177.http://dx.doi.org/10.1002/cem.1131
 Hoskuldsson, A. (1994) Data Analysis, Matrix Decompositions and Generalised Inverse. SIAM Journal on Scientific Computing, 15, 239-262. http://dx.doi.org/10.1137/0915018
 Clinical and Laboratory Standards Institute. http://www.clsi.org
 Kennard, R.W. and Stone, L.A. (1969) Computer Aided Design of Experiment. Technometrics, 11, 43-64. http://dx.doi.org/10.1080/00401706.1969.10490666
 Siotani, M., Hayakawa, T. and Fujikoshi, Y. (1985) Modern Multivariate Analysis: A Graduate Course and Handbook. American Science Press, Columbus.
 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. http://dx.doi.org/10.1016/j.chemolab.2010.10.003
 Hoskuldsson, A. (2001) Variable and Subset Selection in PLS Regression. Chemometrics and Intelligent Laboratory Systems, 557, 23-38. http://dx.doi.org/10.1016/S0169-7439(00)00113-1
 Reinikainen, S.-P. and Hoskuldsson, A. (2003) COVPROC Method: Strategy in Modeling Dynamic Systems. Journal of Chemometrics, 17, 130-139. http://dx.doi.org/10.1002/cem.770
 Grove, H., et al. (2008) Combination of Statistical Approaches for Analysis of 2-DE Data Gives Complementary Results. Proteome Research, 7, 5119-5124.
 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. http://dx.doi.org/10.1016/j.jfoodeng.2008.06.037
 Tapp, H.S., et al. (2012) Evaluation of Multiple Variate Methods from a Biological Perspective: A Nutrigenomics Case Study. Genes & Nutrition, 7, 387-397. http://dx.doi.org/10.1007/s12263-012-0288-4
 Bruker Optics, Germany. http://www.bruker.de
 Micro-Biolytics, Germany.
 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. http://dx.doi.org/10.1016/j.talanta.2013.01.035