relative absolute error

rae.numeric

R Documentation

Description

The rae()-function calculates the normalized relative absolute error between the predicted and observed <numeric> vectors. The weighted.rae() function computes the weigthed relative absolute error.

Usage

## S3 method for class 'numeric'
rae(actual, predicted, ...)

## S3 method for class 'numeric'
weighted.rae(actual, predicted, w, ...)

rae(...)

weighted.rae(...)

Arguments

actual	A <numeric>-vector of length \(n\). The observed (continuous) response variable.
predicted	A <numeric>-vector of length \(n\). The estimated (continuous) response variable.
…	Arguments passed into other methods.
w	A <numeric>-vector of length \(n\). The weight assigned to each observation in the data.

Value

A <numeric> vector of length 1.

Calculation

The Relative Absolute Error (RAE) is calculated as:

\[ \text{RAE} = \frac{\sum_{i=1}^n |y_i - \upsilon_i|}{\sum_{i=1}^n |y_i - \bar{y}|} \]

Where \(y_i\) are the actual values, \(\upsilon_i\) are the predicted values, and \(\bar{y}\) is the mean of the actual values.

Examples

# 1) fit a linear
# regression
model <- lm(
  mpg ~ .,
  data = mtcars
)

# 1.1) define actual
# and predicted values
# to measure performance
actual    <- mtcars$mpg
predicted <- fitted(model)

# 2) evaluate in-sample model
# performance using Relative Absolute Error (RAE)
cat(
  "Relative Absolute Error", rae(
    actual    = actual,
    predicted = predicted,
  ),
  "Relative Absolute Error (weighted)", weighted.rae(
    actual    = actual,
    predicted = predicted,
    w         = mtcars$mpg/mean(mtcars$mpg)
  ),
  sep = "\n"
)