Open AccessAssessing the accuracy of predictive models for numerical data: Not r nor r2, why not? Then what?
Author(s) -
Jin Li
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0183250
Subject(s) - measure (data warehouse) , variance (accounting) , computer science , predictive modelling , accuracy and precision , pearson product moment correlation coefficient , data mining , statistics , predictive validity , mean squared prediction error , correlation , observational error , quality (philosophy) , moment (physics) , mathematics , machine learning , philosophy , physics , geometry , accounting , epistemology , classical mechanics , business
Assessing the accuracy of predictive models is critical because predictive models have been increasingly used across various disciplines and predictive accuracy determines the quality of resultant predictions. Pearson product-moment correlation coefficient ( r ) and the coefficient of determination ( r 2 ) are among the most widely used measures for assessing predictive models for numerical data, although they are argued to be biased, insufficient and misleading. In this study, geometrical graphs were used to illustrate what were used in the calculation of r and r 2 and simulations were used to demonstrate the behaviour of r and r 2 and to compare three accuracy measures under various scenarios. Relevant confusions about r and r 2 , has been clarified. The calculation of r and r 2 is not based on the differences between the predicted and observed values. The existing error measures suffer various limitations and are unable to tell the accuracy. Variance explained by predictive models based on cross-validation ( VEcv ) is free of these limitations and is a reliable accuracy measure. Legates and McCabe’s efficiency ( E 1 ) is also an alternative accuracy measure. The r and r 2 do not measure the accuracy and are incorrect accuracy measures. The existing error measures suffer limitations. VEcv and E 1 are recommended for assessing the accuracy. The applications of these accuracy measures would encourage accuracy-improved predictive models to be developed to generate predictions for evidence-informed decision-making.