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

2022/07/19 by Timothy Hodson · 20 citations
Mathematics · #Advanced Statistical Methods and Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.5194/gmd-15-5481-2022

openalex publication_date 2022/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Abstract. The root-mean-squared error (RMSE) and mean absolute error (MAE) 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 which is more relevant. In a recent reprise to the 200-year debate over their use, Willmott and Matsuura (2005) and Chai and Draxler (2014) give arguments for favoring one metric or the other. However, this comparison can present a false dichotomy. Neither metric is inherently better: RMSE is optimal for normal (Gaussian) errors, and MAE is optimal for Laplacian errors. When errors deviate from these distributions, other metrics are superior.

Cited by

• The Pick-the-Winner-Picker Heuristic: Preference for Categorically Correct Forecasts
• Comparative analysis of different prediction methods for TEC in China based on deep learning
• Building Network Digital Twins Part II: Real-Time Adaptive PID for Enhanced State Synchronization
• Automatic essay scoring: leveraging Jaccard coefficient and Cosine similaritywith n-gram variation in vector space model approach
• A Compositional Approach to Modelling Cause-specific Mortality with Zero Counts
• Sketch2BIM: A Multi-Agent Human-AI Collaborative Pipeline to Convert Hand-Drawn Floor Plans to 3D BIM
• MolGA: Molecular Graph Adaptation with Pre-trained 2D Graph Encoder
• Age estimation through CT image analysis of the thoracic cage in a Mediterranean population
• Advancing regional water quality modelling: integrating spatial machine learning with large-scale catchment data
• A Data-Driven Framework for Digital Transformation in Smart Cities: Integrating AI, Dashboards, and IoT Readiness
• A custom‐built single‐channel in‐ear electroencephalography sensor for sleep phase detection: an interdependent solution for at‐home sleep studies
• Multi-scale dynamic population estimation: an Adaptive Inverse Distance Weighting (AIDW) model incorporating spatial characteristics
• Communications to Circulations: Real-Time 3D Wind Field Prediction Using 5G GNSS Signals and Deep Learning
• Distribution Shift Aware Neural Tabular Learning
• Hierarchical Evaluation Function: A Multi-Metric Approach for Optimizing Demand Forecasting Models
• User Trajectory Prediction Unifying Global and Local Temporal Information
• Exploring the potential of two vegetative indices, normalized difference vegetation index (NDVI) and enhanced vegetation index 2 (EVI2), to estimate balsam fir nutrition using uncrewed aerial vehicles and multispectral sensing
• Glucose-ML: A collection of longitudinal diabetes datasets for development of robust AI solutions
• Comparison of the Performance of Fluorescent, Phosphorescent, and TADF Luminophores for Explosives Sensing
• Predicting lignin removal efficiency in deep eutectic solvent-based biomass fractionation: an explainable machine learning approach

Related

• Using the Mean Absolute Percentage Error for Regression Models
• Empirical risk minimization is consistent with the mean absolute percentage error
• The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation
• An Investigation of the Sample Performance of Two Nonnormality Corrections for RMSEA
• The Performance of RMSEA in Models With Small Degrees of Freedom