Construct a B-spline basis matrix

Build a B-spline basis for a numeric vector using a Cox-de Boor style recursion. By default, the function constructs a cubic spline basis (P = 3) and chooses the number of basis functions from the number of unique values in x.

Usage

s(
  x,
  P = 3,
  K = min(7, max(3, floor(log2(length(unique(x)))))),
  limits = c(NA, NA),
  knots = "eq"
)

Arguments

x: A numeric vector of predictor values.
P: A non-negative integer giving the spline degree. P = 3 corresponds to a cubic B-spline basis.
K: An integer giving the number of basis functions to return. The default increases slowly with the number of unique values in x.
limits: A numeric vector of length 2 giving the lower and upper boundary limits for the spline basis. Missing values are replaced by min(x) and max(x).
knots: Either a numeric vector of knot locations, or one of "eq" or "quantile". If "eq", knots are placed uniformly between limits[1] and limits[2]. If "quantile", knots are placed at equally spaced empirical quantiles of x.

Value

A numeric matrix with one row per element of x and one column per spline basis function.

Details

Boundary limits are taken from x unless supplied explicitly. Knot locations may be given directly as a numeric vector, or generated either at equally spaced locations ("eq") or at empirical quantiles ("quantile").

The returned basis has length(x) rows and k columns.

When knots is generated internally, the function first creates K - P + 1 knot locations and then augments them with repeated boundary knots so the recursion can be evaluated.

Examples

x <- seq(0, 1, length.out = 10)

# Default cubic basis
B <- s(x)
dim(B)
#> [1] 10  3

# Equally spaced knots with custom basis size
B2 <- s(x, K = 5, knots = "eq")

# Quantile-based knots
B3 <- s(x, knots = "quantile")