Measures of Accuracy

Some measures of model accuracy like mean absolute error (MAE), mean absolute percentage error (MAPE), symmetric mean absolute percentage error (SMAPE), mean squared error (MSE) and root mean squared error (RMSE).

MAE(x, ...)
# Default S3 method
MAE(x, ref, na.rm = FALSE, ...)
# S3 method for class 'lm'
MAE(x, ...)

MAPE(x, ...)
# Default S3 method
MAPE(x, ref, na.rm = FALSE, ...)
# S3 method for class 'lm'
MAPE(x, ...)

SMAPE(x, ...)
# Default S3 method
SMAPE(x, ref, na.rm = FALSE, ...)
# S3 method for class 'lm'
SMAPE(x, ...)

MSE(x, ...)
# Default S3 method
MSE(x, ref, na.rm = FALSE, ...)
# S3 method for class 'lm'
MSE(x, ...)

RMSE(x, ...)
# Default S3 method
RMSE(x, ref, na.rm = FALSE, ...)
# S3 method for class 'lm'
RMSE(x, ...)


NMAE(x, ref, train.y)
NMSE(x, ref, train.y)

Arguments

x

the predicted values of a model or a model-object itself.

ref

the observed true values.

train.y

the observed true values in a train dataset.

na.rm

a logical value indicating whether or not missing values should be removed. Defaults to FALSE.

...

further arguments

Details

The function will remove NA values first (if requested).
MAE calculates the mean absolute error: $$\frac{1}{n} \cdot \sum_{i=1}^{n}\left | ref_{i}-x_{i} \right |$$

MAPE calculates the mean absolute percentage error: $$\frac{1}{n} \cdot \sum_{i=1}^{n}\left | \frac{ref_{i}-x_{i}}{ref_{i}} \right |$$

SMAPE calculates the symmetric mean absolute percentage error: $$\frac{1}{n} \cdot \sum_{i=1}^{n}\frac{2 \cdot \left | ref_{i}-x_{i} \right |}{\left | ref_{i} \right | + \left | x_{i} \right |}$$

MSE calculates mean squared error: $$\frac{1}{n} \cdot \sum_{i=1}^{n}\left ( ref_{i}-x_{i} \right )^2$$

RMSE calculates the root mean squared error: $$\sqrt{\frac{1}{n} \cdot \sum_{i=1}^{n}\left ( ref_{i}-x_{i} \right )^2}$$

Value

the specific numeric value

References

Armstrong, J. S. (1985) Long-range Forecasting: From Crystal Ball to Computer, 2nd. ed. Wiley. ISBN 978-0-471-82260-8
https://en.wikipedia.org/wiki/Symmetric_mean_absolute_percentage_error

Torgo, L. (2010) Data Mining with R: Learning with Case Studies, Chapman and Hall/CRC Press

Author

Andri Signorell <andri@signorell.net>

See also

lm, resid

Examples

r.lm <- lm(Fertility ~ ., data=swiss)

MAE(r.lm)
#> [1] 5.32138

# the same as:
MAE(predict(r.lm), swiss$Fertility)
#> [1] 5.32138

MAPE(r.lm)
#> [1] 0.07857082
MSE(r.lm)
#> [1] 44.78815
RMSE(r.lm)
#> [1] 6.692395