Content of this repository

This repository is a tool to supports my research: evaluating and visualizing model performance.

Input:

• At minimum, you need to provide two vectors:
  • true: observed (actual) values
  • pred: predicted values
• Optional inputs allow you to control the number of decimal places for statistics and whether to generate plots.

Output:

• The main function (gfit.py) returns a set of goodness-of-fit statistics, including MSE, RMSE, MAE, R², correlation, bias, and more.
• Optionally, you can generate plots to visualize model performance:
  • 1:1 scatter plot (predicted vs. observed)
  • Q-Q plot of residuals
  • Residual plot

The respository contains two files:

• gfit.py: the main analysis function
• README.md: this overview and usage guide

Considered goodness-of-fit statistics

10 statistics are included in this function "gfit.py". They are:

• MSE: Mean Squared Error. Square of the unit of the output variable.
  Measures the average squared difference between observed and predicted values. Lower values indicate better fit.
• RMSE: Root Mean Square Error. The unit is the same as output variable.
  The square root of MSE; shows the average error in the same units as the data.
• Bias: Bias. The unit is the same as output variable.
  The average difference between predicted and observed values. Indicates if predictions are systematically too high or too low.
• r: Correlation coefficient. Unitless.
  Measures the strength and direction of the linear relationship between observed and predicted values (ranges from -1 to 1).
• p-value: p-value. Unitless.
  
  • It tells how likely it is that the result happened by random chance.
  • A small p-value (usually less than 0.05) means the result is probably not just random, so there is likely a real effect of relationship.
  • A large p-value means the result could esaily happen by chance, so there may not be a real effect.
• d: Willmoot's index of agreement. Unitless.
  Measures the degree of model prediction error (ranges from 0 to 1, with 1 being perfect agreement).
• R2: Coefficient of determination. Unitless.
  Shows the proportion of variance in observed values explained by the predictions (ranges from 0 to 1).
• MAE: Mean Absolute Error. The unit is the same as output variable.
  The average of the absolute differences between observed and predicted values.
• RRMSE: Relative Root Mean Square Error. %.
  RMSE expressed as a percentage of the mean observed value.
• RSD: The standard deviation of the residual. The unit is the same as output variable.
  Indicates how spread out the residuals (errors)

Citation

If you also use this repository in your work, please cite it using the following DOI:

BibTeX:

@misc{gao2025goodfit,
  author       = {Rui Gao},
  title        = {Goodness of Fit Model},
  year         = {2025},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.16700596},
  url          = {https://doi.org/10.5281/zenodo.16700596}
}

Contact information is issues were found:

Any found issues are appreciated to contact Rui at
Rui.Ray.Gao@gmail.com
RuiGao@UCMerced.edu