Preprints
https://doi.org/10.5194/gmd-2022-64
https://doi.org/10.5194/gmd-2022-64
Submitted as: review and perspective paper
11 Mar 2022
Submitted as: review and perspective paper | 11 Mar 2022
Status: a revised version of this preprint is currently under review for the journal GMD.

Root mean square error (RMSE) or mean absolute error (MAE): when to use them or not

Timothy O. Hodson Timothy O. Hodson
  • U.S. Geological Survey Central Midwest Water Science Center, Urbana, IL

Abstract. The mean absolute error (MAE) and root mean squared error (RMSE) are widely used metrics for evaluating models. Yet, there remains enduring confusion over their use, such that a standard practice is to present both, leaving it to the reader to decide. Some of this confusion arises from a recent debate between Willmott and Draxler (2005) and Chai and Draxler (2014), in which either side presents their arguments for one metric over the other. Neither side was completely correct; however, because neither metric is inherently better: MAE is optimal for Laplacian errors, and RMSE is optimal for normal (Gaussian) errors. When errors deviate from these distributions, other metrics are superior.

Timothy O. Hodson

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2022-64', Anonymous Referee #1, 08 Apr 2022
    • AC1: 'Reply on RC1', Timothy Hodson, 12 Apr 2022
    • AC2: 'Reply on RC1 (Ammendment)', Timothy Hodson, 15 Apr 2022
  • RC2: 'Comment on gmd-2022-64', Anonymous Referee #2, 21 Apr 2022
    • AC3: 'Reply on RC2', Timothy Hodson, 26 Apr 2022

Timothy O. Hodson

Timothy O. Hodson

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Short summary
The task of selecting explanatory models is fundamental in the scientific process. The “best” models are identified using an objective metric, the choice which ultimately determines what scientists learn from their data. The mean absolute error (MAE) and root mean squared error (RMSE) are two such metrics. Both are widely used, yet there remains enduring confusion over their use. This article reviews the theoretical argument behind their usage, as well as alternatives for when they fail.