What is Normalized Root Mean Square Error (NRMSE)?

Normalized Root Mean Square Error (NRMSE) measures the accuracy of a predictive model by comparing the predicted values to the observed values, normalized by the range, mean, or standard deviation of the observed data. It provides a standardized way to evaluate model performance across different datasets.

Formula

A model predicts the temperatures for a week. The observed temperatures range from 50⁰F to 90⁰F. If the RMSE is 5⁰F, the NRMSE is:

NRMSE= RMSE / Xmax- Xmin

where RMSE (Root Mean Square Error) is calculated as:

Example

A model predicts the temperatures for a week. The observed temperatures range from 50⁰F to 90⁰F. If the RMSE is 5⁰F, the NRMSE is:

NRMSE=5 / 90 – 50= 0.125

This means the RMSE is 12.5% of the range of observed temperatures.

Why is Normalized Root Mean Square Error (NRMSE) important?

NRMSE is crucial for:

• Providing a standardized metric to compare model performance across different scales.
• Highlighting the accuracy of predictive models.
• Facilitating easier interpretation of error relative to the data range.
• Enhancing model selection and optimization processes.

Which factors impact Normalized Root Mean Square Error (NRMSE)?

Several factors can influence NRMSE, including:

• Data Quality: Accuracy and completeness of the observed data.
• Model Complexity: The complexity and appropriateness of the predictive model.
• Outliers: Presence of outliers can disproportionately affect RMSE and NRMSE.
• Normalization Method: Choice of normalization (range, mean, standard deviation).

How can Normalized Root Mean Square Error (NRMSE) be improved?

Several factors can influence NRMSE, including:

• Data Quality: Accuracy and completeness of the observed data.
• Model Complexity: The complexity and appropriateness of the predictive model.
• Outliers: Presence of outliers can disproportionately affect RMSE and NRMSE.
• Normalization Method: Choice of normalization (range, mean, standard deviation).

What is Normalized Root Mean Square Error (NRMSE)’s relationship with other metrics?

NRMSE is closely related to metrics like RMSE, MAE (Mean Absolute Error), and R-squared. While RMSE provides the absolute error measure, NRMSE standardizes this error, making it more interpretable and comparable across datasets. It complements these metrics by offering a normalized view of model accuracy, essential for robust model evaluation and comparison.