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Compute Area Under the Curve

Source: R/auc.R
auc.Rd

Calculates the area under a curve defined by points (x, y) using different numerical integration methods.

Usage

auc(
  x,
  y,
  from = min(x, na.rm = TRUE),
  to = max(x, na.rm = TRUE),
  method = c("trapezoid", "step", "spline"),
  absoluteArea = FALSE,
  subdivisions = 100,
  na.rm = FALSE,
  ...
)

Arguments

x, y

numeric vectors of equal length defining the curve coordinates

from, to

single numeric values specifying the integration interval; by default, the range of x

method

character string specifying the integration method: "trapezoid", "step", or "spline"

absoluteArea

logical; whether areas below zero are counted as positive

subdivisions

positive whole number specifying the maximum number of subdivisions used for spline integration

na.rm

logical; whether incomplete (x, y) pairs are removed

...

additional arguments passed to stats::approx() for trapezoidal interpolation

Value

a numeric value representing the computed area

Details

The available methods are:

  • "trapezoid": linear interpolation between successive points

  • "step": a right-continuous step function using the value at the left endpoint of each interval

  • "spline": a natural cubic spline integrated numerically

For method = "step", an integration boundary lying between two observed x values retains the value of the preceding point. No linear interpolation is performed at the boundary.

If absoluteArea = TRUE, the absolute value of the interpolated curve is integrated. Sign changes in linear segments are split at their exact zero-crossing. For the step method, the absolute values of the constant step heights are used.

Both integration limits must lie inside the range of x. Extrapolation is not performed.

See also

stats::approx(), stats::splinefun(), stats::integrate()

Other model.metrics: averagePrecision(), brierScore(), logLoss(), mae(), mape(), mse(), nmae(), nmse(), rmse(), smape()

Examples

x <- c(1, 2, 3, 5)
y <- c(0, 1, 1, 2)

auc(x, y)
#> [1] 4.5
auc(x, y, method = "step")
#> [1] 3
auc(x, y, method = "spline")
#> [1] 4.347826
auc(x, y, absoluteArea = TRUE)
#> [1] 4.5

# interval boundaries between observed x values
auc(
  x = c(0, 1, 2),
  y = c(-2, 10, 4),
  from = 0.5,
  to = 1.5,
  method = "step"
)
#> [1] 4

auc(
  x = c(0, 1, 2),
  y = c(-2, 10, 4),
  from = 0.5,
  to = 1.5,
  method = "step",
  absoluteArea = TRUE
)
#> [1] 6