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Computational and Mathematical Methods in Medicine
Volume 2016 (2016), Article ID 8578156, 8 pages
http://dx.doi.org/10.1155/2016/8578156
Research Article

Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error

1Department of Physics and Chemistry, Faculty of Materials and Environmental Engineering, Technical University of Cluj-Napoca, Muncii Boulevard No. 103-105, 400641 Cluj-Napoca, Romania
2Doctoral School of Chemistry, Institute for Doctoral Studies, Babeş-Bolyai University, Kogălniceanu Street No. 1, 400084 Cluj-Napoca, Romania
3Department of Chemistry, Faculty of Science, University of Oradea, Universităţii Street No. 1, 410087 Oradea, Romania
4Department of Medical Informatics and Biostatistics, Faculty of Medicine, Iuliu Haţieganu University of Medicine and Pharmacy, Louis Pasteur Street No. 6, 400349 Cluj-Napoca, Romania
5Doctoral School, University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca, Calea Mănăştur No. 3-5, 400372 Cluj-Napoca, Romania

Received 22 August 2016; Accepted 23 October 2016

Academic Editor: Irini Doytchinova

Copyright © 2016 Lorentz Jäntschi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for finding the coefficients on linear models with two predictors without any constrictive assumptions on the distribution of the errors. The algorithm was developed, implemented, and tested as proof-of-concept using fourteen sets of compounds by investigating the link between activity/property (as outcome) and structural feature information incorporated by molecular descriptors (as predictors). The results on real data demonstrated that in all investigated cases the power of the error is significantly different by the convenient value of two when the Gauss-Laplace distribution was used to relax the constrictive assumption of the normal distribution of the error. Therefore, the Gauss-Laplace distribution of the error could not be rejected while the hypothesis that the power of the error from Gauss-Laplace distribution is normal distributed also failed to be rejected.