impute_quantiles: Impute additional quantiles from a 'quantile_pred'

In hardhat: Construct Modeling Packages

Impute additional quantiles from a quantile_pred

Description

While a quantile_pred describes evaluations for the inverse cummulative distribution function (CDF, sometimes called the "quantile function") at particular quantile levels, this is not enough to fully describe the distribution. For example,

p <- c(.1, .5, .9)
quantile_pred(matrix(qnorm(p), nrow = 1), p)

encapsulates the 10%, 50%, and 90% quantile levels of the standard normal distribution. But, what if we need, say, the 25% and 75% levels? This function imputes them if possible.

Usage

impute_quantiles(
  x,
  probs,
  lower = -Inf,
  upper = Inf,
  middle = c("cubic", "linear")
)

Arguments

x	an object of class quantile_pred
probs	vector. probabilities at which to evaluate the inverse CDF
lower	number. lower bound for the resulting values
upper	number. upper bound for the resulting values
middle	character. if middle = 'cubic' (the default), a cubic spline is used for interpolation where possible; middle='linear' interpolates linearly; see Details below.

Details

If probs is simply a subset of quantile_levels that already exist in x, then these will be returned (up to numeric error). Small errors are possible due to difficulties matching double vectors.

For probs that do not exist in x, these will be interpolated or extrapolated as needed. The process has 3 steps.

First, by default (middle = "cubic"), missing internal quantile levels are interpolated using a cubic spline fit to the observed values + quantile levels with stats::splinefun. Second, if cubic interpolation fails (or if middle = "linear"), linear interpolation is used via stats::approx. Finally, missing external quantile levels (those outside the range of quantile_levels) are extrapolated. This is done using a linear fit on the logistic scale to the two closest tail values.

This procedure results in sorted quantiles that interpolate/extrapolate smoothly, while also enforcing heavy tails beyond the range.

Optionally, the resulting quantiles can be constrained to a compact interval using lower and/or upper. This is done after extrapolation, so it may result in multiple quantile levels having the same value (a CDF with a spike).

Value

A matrix with length(probs) columns and length(x) rows. Each row contains the inverse CDF (quantile function) given by x, extrapolated/interpolated to probs.

Examples

p <- c(.1, .5, .9)
qp <- quantile_pred(matrix(c(qnorm(p), qexp(p)), nrow = 2, byrow = TRUE), p)
impute_quantiles(qp, p)
as.matrix(qp) # same as the imputation

p1 <- c(.05, .25, .75, .95)
impute_quantiles(qp, p1)
rbind(qnorm(p1), qexp(p1)) # exact values, for comparison

hardhat documentation built on April 4, 2026, 5:07 p.m.