Applicability of the ACE algorithm for multiple regression in hydrogeology

• Published in: Computational geosciences Vol. 13; no. 1; pp. 123 - 134
• Main Authors: Szucs, Peter, Horne, Roland N.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2009; Springer Nature B.V
• Subjects: Algorithms; Earth and Environmental Science; Earth Sciences; Geology; Geotechnical Engineering & Applied Earth Sciences; Groundwater data; Hydrogeology; Hydrologic data; Hydrology; Mathematical Modeling and Industrial Mathematics; Original Paper; Soil Science & Conservation; Studies; Alternating conditional expectation; Hydrogeology; Most frequent value; Nonparametric approach; Multiple regression
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-008-9112-z

This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (J Am Stat Assoc 80:580–619, 1985 ) for estimating the transformations of a response and a set of predictor variables in multiple regression problems in hydrogeology. The proposed nonparametric approach can be applied easily for estimating the optimal transformations of different hydrogeological data to obtain maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. The advantages and applicability of this new approach to solve different multiple regression problems in hydrogeology or in Earth Sciences are illustrated by means of theoretical investigations and case studies. It is demonstrated that the ACE method has certain advantages in some fitting problems of hydrogeology over the traditional multiple regression. Based on our knowledge, this is the first application of the ACE algorithm to analyze and interpret groundwater data.