Build an additive design matrix for GAMs

Constructs the expanded design matrix for generalized additive models by appending spline basis terms according to per-column specifications. Each column in X keeps its linear term; columns with a non-NULL specification get additional spline basis columns appended.

This function mirrors additive_design_matrix() in Python delicatessen, so code translated from Python can keep its shape. There is no base R equivalent of this construction, so this is the interface for it in deli as well.

Usage

additive_design_matrix(X, specifications, return_penalty = FALSE)

Arguments

X

Numeric matrix (n-by-b) of input covariates.

specifications

A list of length b (number of columns in X). Each element is either NULL (no spline for that column) or a list with:

knots

Numeric vector of knot locations (required).

natural

Logical, generate restricted splines? Default TRUE.

power

Numeric power for spline. Default 3.

penalty

Numeric penalty for spline terms. Default 0.

normalized

Logical, normalize spline terms? Default FALSE.

return_penalty

Logical. If TRUE, return a list with both the design matrix and the penalty vector. Default FALSE.

Value

If return_penalty = FALSE, a numeric matrix. If TRUE, a list with elements X (the design matrix) and penalty (numeric vector).

Examples

set.seed(42)
X <- cbind(rnorm(50), rnorm(50))

# The first column stays linear; the second also gets penalized splines
specs <- list(NULL, list(knots = c(-1, 0, 1), penalty = 5))
out <- additive_design_matrix(X, specs, return_penalty = TRUE)

# Linear terms are unpenalized, spline terms carry the requested penalty
out$penalty
#> [1] 0 0 5 5

dim(out$X)
#> [1] 50  4