Regression Metrics

Case-weighted versions of typical regression metrics:

• mse(): Mean-squared error.

• rmse(): Root-mean-squared error.

• mae(): Mean absolute error.

• medae(): Median absolute error.

• mape(): Mean absolute percentage error.

• prop_within(): Proportion of predictions that are within a given tolerance around the actual values.

• deviance_normal(): Average (unscaled) normal deviance. Equals MSE, and also the average Tweedie deviance with \(p = 0\).

• deviance_poisson(): Average (unscaled) Poisson deviance. Equals average Tweedie deviance with \(p=1\).

• deviance_gamma(): Average (unscaled) Gamma deviance. Equals average Tweedie deviance with \(p=2\).

• deviance_tweedie(): Average Tweedie deviance with parameter \(p \in \{0\} \cup [1, \infty)\), see reference.

Lower values mean better performance. Notable exception is prop_within(), where higher is better.

mse(actual, predicted, w = NULL, ...)

rmse(actual, predicted, w = NULL, ...)

mae(actual, predicted, w = NULL, ...)

medae(actual, predicted, w = NULL, ...)

mape(actual, predicted, w = NULL, ...)

prop_within(actual, predicted, w = NULL, tol = 1, ...)

deviance_normal(actual, predicted, w = NULL, ...)

deviance_poisson(actual, predicted, w = NULL, ...)

deviance_gamma(actual, predicted, w = NULL, ...)

deviance_tweedie(actual, predicted, w = NULL, tweedie_p = 0, ...)

Arguments

actual

Observed values.

predicted

Predicted values.

w

Optional case weights.

...

Further arguments passed to weighted_mean() (no effect for medae()).

tol

Predictions in \([\textrm{actual} \pm \textrm{tol}]\) count as "within" (only relevant for prop_within()).

tweedie_p

Tweedie power \(p \in \{0\} \cup [1, \infty)\).

Value

A numeric vector of length one.

Input range

The values of actual and predicted can be any real numbers, with the following exceptions:

• mape(): Non-zero actual values.

• deviance_poisson(): Non-negative actual values and predictions.

• deviance_gamma(): Strictly positive actual values and predictions.

References

Jorgensen, B. (1997). The Theory of Dispersion Models. Chapman & Hall/CRC. ISBN 978-0412997112.

Examples

y <- 1:10
pred <- c(1:9, 12)
w <- 1:10

rmse(y, pred)
#> [1] 0.6324555
sqrt(mse(y, pred))  # Same
#> [1] 0.6324555

mae(y, pred)
#> [1] 0.2
mae(y, pred, w = w)
#> [1] 0.3636364
medae(y, pred, w = 1:10)
#> [1] 0
mape(y, pred)
#> [1] 2

prop_within(y, pred)
#> [1] 0.9

deviance_normal(y, pred)
#> [1] 0.4
deviance_poisson(y, pred)
#> [1] 0.03535689
deviance_gamma(y, pred)
#> [1] 0.003130978

deviance_tweedie(y, pred, tweedie_p = 0)  # Normal
#> [1] 0.4
deviance_tweedie(y, pred, tweedie_p = 1)  # Poisson
#> [1] 0.03535689
deviance_tweedie(y, pred, tweedie_p = 2)  # Gamma
#> [1] 0.003130978
deviance_tweedie(y, pred, tweedie_p = 1.5, w = 1:10)
#> [1] 0.01912556