title: A new approach in regression analysis for modeling adsorption isotherms.
abstract: Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.
authors.affiliation: Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
authors.forename: Dana D
authors.identifier: 0000-0002-6033-5457
authors.initials: DD
authors.lastname: Marković
authors.affiliation: Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia.
authors.forename: Branislava M
authors.identifier: 0000-0002-3360-2118
authors.initials: BM
authors.lastname: Lekić
authors.affiliation: Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia.
authors.forename: Vladana N
authors.identifier: 0000-0003-4895-7007
authors.initials: VN
authors.lastname: Rajaković-Ognjanović
authors.affiliation: Vinča Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia.
authors.forename: Antonije E
authors.initials: AE
authors.lastname: Onjia
authors.affiliation: Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia.
authors.forename: Ljubinka V
authors.identifier: 0000-0002-5765-8634
authors.initials: LV
authors.lastname: Rajaković
mesh_terms: D000327:Adsorption; D000465:Algorithms; D016018:Least-Squares Analysis; D008962:Models, Theoretical; D012044:Regression Analysis; D013696:Temperature