The choice between RMSE (Root Mean Squared Error) and MAE (Mean Absolute Error) as a metric for evaluating a regression model depends on several factors, including the characteristics of the data and the specific goals of your analysis. Here are some considerations for when to use RMSE over MAE and vice versa:
Use RMSE when:
Outliers Matter: RMSE is more sensitive to outliers than MAE. If you want the model to heavily penalize larger prediction errors (which is often the case when outliers have a significant impact on the overall performance), RMSE is a better choice. It squares the errors, giving higher weight to larger deviations from the true values.
Gaussian Assumption: RMSE assumes that errors are normally distributed. If your data follows a Gaussian distribution, RMSE may be more appropriate, as it aligns with the underlying assumptions.
Relative Error Matters: RMSE provides a measure of the average relative error. It is a good choice when you want to compare models in terms of their relative performance, giving more weight to predictions that are relatively far from the true values.
Differentiating Models: RMSE tends to emphasize larger errors, making it useful when you want to differentiate between models that perform well on most data points but have varying levels of performance on specific data points.
Use MAE when:
Robustness to Outliers: MAE is less sensitive to outliers compared to RMSE. If you want the model's performance metric to be more robust in the presence of outliers, MAE is a better choice.
Absolute Error Matters: MAE provides a straightforward measure of the average absolute error. It is a good choice when you want to report errors in the same units as the target variable, making it more interpretable.
Symmetry of Error: If the positive and negative errors have equal importance (i.e., overestimation and underestimation are equally penalized), MAE is a suitable choice.
Ease of Interpretation: MAE is easier to interpret because it directly represents the average magnitude of errors in the original units of the target variable. It's particularly useful when you need to communicate model performance to non-technical stakeholders.
In practice, it's often a good idea to consider both RMSE and MAE, along with other relevant metrics, when evaluating a regression model. The choice between the two should align with the specific goals of your analysis and the characteristics of your data, particularly its distribution and the presence of outliers. Additionally, domain-specific considerations may also influence the choice between RMSE and MAE.