Multiple linear regressions by maximizing the likelihood under assumption of generalized Gauss-Laplace distribution of the error
type: Item
instance of: scholarly article
title: Multiple linear regressions by maximizing the likelihood under assumption of generalized Gauss-Laplace distribution of the error
zbMATH Open document ID: 1368.92010
DOI: 10.1155/2016/8578156
author: Lorentz Jäntschi
author: Donatella Bálint
author: Sorana D. Bolboacă
published in: Computational \& Mathematical Methods in Medicine
publication date: 2017-08-10T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92B15
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 6759158
zbMATH Keywords: multiple linear regression
zbMATH Keywords: Gauss-Laplace distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/8578156
OpenAlex ID: W2559981017
Wikidata QID: Q39019251
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DBLP publication ID: journals/cmmm/JantschiBB16
description: scientific article; zbMATH DE number 6759158