GeDS (version 0.2.8)

PPolyInv: Inversion the piecewise polynomial representation of a spline object

Description

Computes the inverse mapping of a piecewise polynomial spline object. Given a strictly monotonic spline (produced by PPolyRep or similar), the function returns the corresponding predictor values for a new set of response values.

Usage

PPolyInv(ppoly, y_new)

Value

A numeric vector (or column matrix) of predictor values corresponding to the input y_new values.

Arguments

ppoly

A spline object of class "npolySpline", "polySpline", or "spline" that represents a piecewise polynomial form. The spline must be strictly monotonic (either increasing or decreasing) to allow for inversion.

y_new

A numeric vector of response values for which the corresponding predictor values are sought.

Details

PPolyInv first verifies that the supplied ppoly object is invertible by checking its strict monotonicity via the helper function is_invertible. If the spline is not strictly monotonic, the function stops with an error.

The function extracts the knot locations and polynomial coefficients from ppoly to build a data frame of polynomial segments. For each value in y_new, it identifies the correct interval and uses the helper function solve_x to solve the corresponding polynomial equation for the predictor value.

Examples

# Generate a data sample for the response variable
# Y and the single covariate X
set.seed(123)
N <- 1000
f_1 <- function(x) x^3
X <- sort(runif(N, min = -5, max = -3))
# Specify a model for the mean of Y to include only a component
# non-linear in X, defined by the function f_1
means <- f_1(X)
# Add (Normal) noise to the mean of Y
Y <- rnorm(N, means, sd = 0.2)

Gmod <- NGeDS(Y ~ f(X), phi = 0.9)

plot(Gmod)

# Convert GeDS fit to a cubic piecewise polynomial representation
ppoly <- PPolyRep(Gmod, n = 4)
# Invert the spline using predicted values to recover predictor values
pred_new <- Gmod$Cubic.Fit$Predicted
X_new <- PPolyInv(ppoly, pred_new)
# Compare recovered predictors to original values (differences should be near 0)
as.numeric(round(X_new - X, 4))