Calibrate an interval whose width is a fitted scale.

Usage

conformal_scaled_calibrate(
  obs,
  pred,
  covariates,
  alpha = 0.1,
  fit_frac = 0.5,
  floor_frac = 0.05,
  seed = 42L,
  scale = NULL,
  group = NULL
)

Arguments

obs, pred: Calibration observations and predictions, NATIVE units.
covariates: A data frame of scale covariates, one row per point, e.g. data.frame(level = pred, di = di). The scale is a + b1 x1 + b2 x2 + ..., fitted by least squares on |obs - pred|.
alpha: Miscoverage rate: 0.1 asks for 90%.
fit_frac: Share of the points the scale is fitted on; the rest calibrate q. One half each is the textbook split. Not used when scale is given.
floor_frac: The scale is never below this share of the median |residual| of the fitting half. A linear fit can go to zero or below at the edge of the covariates' range, and a zero-width interval there would claim a certainty the data never gave.
seed: Seed of the split.
scale: NULL: the scale is fitted on fit_frac of these points and q taken on the rest. A conformal_scale from conformal_scale_fit(), fitted on OTHER points: every point here then calibrates q.
group: Optional group of each point, as in conformal_calibrate(): q weighs every group alike, and the split, when there is one, keeps a group on one side.

Value

A conformal_scaled (also a conformal_cal).

Examples

set.seed(1)
level <- runif(300, 1, 4)
di    <- runif(300)                      # a dissimilarity index
obs   <- exp(level + rnorm(300, 0, 0.1 + 0.3 * di))
pred  <- exp(level)
covariates <- data.frame(level = pred, di = di)
cal <- conformal_scaled_calibrate(obs[1:200], pred[1:200], covariates[1:200, ],
                                  alpha = 0.1)
cal
#> 
#> <conformal_scaled> 90% intervals, width = q x fitted scale
#>   scale              : -2.7486 +0.2495 x level +4.5165 x di  (floor 0.1124; R2 on the fit half 0.386)
#>   points             : 100 fitted the scale, 100 calibrated q
#>   rank used          : 91 of 100  (the (n+1) correction)
#>   q                  : 3.7964 x scale
# the scale fitted on other points, and all 100 of these calibrating q
sc <- conformal_scale_fit(obs[1:200], pred[1:200], covariates[1:200, ])
conformal_scaled_calibrate(obs[201:300], pred[201:300], covariates[201:300, ],
                           scale = sc)
#> 
#> <conformal_scaled> 90% intervals, width = q x fitted scale
#>   scale              : -2.5489 +0.2269 x level +4.8155 x di  (floor 0.0974; R2 on the fit half 0.338)
#>   points             : 200 fitted the scale (other points), 100 calibrated q
#>   rank used          : 91 of 100  (the (n+1) correction)
#>   q                  : 4.0640 x scale