Internal validation parameters of linear regression equations in QSAR problem

Abstract

The article discusses a set of internal validation parameters that are (or can be) used to describe the quality of regression models in quantitative structure-activity relationship problems. Among these parameters there are well known determination coefficient, root mean square deviation, mean absolute error, etc. Also the indices based at Kullback-Leibler divergence as a measure of distance between two sets have been investigated. All the parameters (indices) were calculated for several regression models which describe boiling point of saturated hydrocarbons (alkanes). Regression models include a four-component additive scheme and equations describing the property as a function of topological indices. The two types of regressions based on these indices are linear dependencies on only one topological index and linear dependencies on topological index and the number of carbon atoms in the hydrocarbon. Various linear regression equations have been described with internal validation parameters that evaluate the quality of the equations from different perspectives. It is shown that a wide set of test parameters is not only an additional yet alternative description of regression models, but also provides the most complete description of the predictive characteristics and quality of the obtained regression model.