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Relative Absolute Error

Source: R/regr_rae.R
rae.Rd

Measure to compare true observed response with predicted response in regression tasks.

Usage

rae(truth, response, na_value = NaN, ...)

Arguments

truth

(numeric())
True (observed) values. Must have the same length as response.

response

(numeric())
Predicted response values. Must have the same length as truth.

na_value

(numeric(1))
Value that should be returned if the measure is not defined for the input (as described in the note). Default is NaN.

...

(any)
Additional arguments. Currently ignored.

Value

Performance value as numeric(1).

Details

The Relative Absolute Error is defined as $$ \frac{\sum_{i=1}^n \left| t_i - r_i \right|}{\sum_{i=1}^n \left| t_i - \bar{t} \right|}, $$ where \(\bar{t} = \sum_{i=1}^n t_i\). This measure is undefined for constant \(t\).

Can be interpreted as absolute error of the predictions relative to a naive model predicting the mean.

Meta Information

  • Type: "regr"

  • Range: \([0, \infty)\)

  • Minimize: TRUE

  • Required prediction: response

See also

Other Regression Measures: ae(), ape(), bias(), ktau(), linex(), mae(), mape(), maxae(), maxse(), medae(), medse(), mse(), msle(), pbias(), pinball(), rmse(), rmsle(), rrse(), rse(), rsq(), sae(), se(), sle(), smape(), srho(), sse()

Examples

set.seed(1)
truth = 1:10
response = truth + rnorm(10)
rae(truth, response)
#> [1] 0.2599162