spliunes {BoomSpikeSlab}

Spline Basis Expansions

Description

Spline basis expansions of a continuous variable.

Usage

  BsplineBasis(x, knots = NULL, numknots = 3)
  MsplineBasis(x, knots = NULL, numknots = 3)
  IsplineBasis(x, knots = NULL, numknots = 3)

  ## S3 method for class 'SplineBasis'
knots(Fn, ...)

Arguments

x

A numeric vector to be expanded.

knots

A numeric vector of knots defining the expansion. The smallest and largest elements in knots defines the range of the expansion. These knots are (notionally) replicated infinitely many times.

numknots

If the knot vector is NULL then create a vector of length numknots that partitions x into numknots + 1 eqiprobable segments.

Fn

A spline basis matrix.

...

Unused, but required to match the signature of the knots generic function in the stats package.

Details

B-splines are the basis most commonly used for additive regression models.

M-splines are an alternative to B-splines, but are rarely used.

I-splines are integrated M-splines. These are monotonic functions, which is useful in monotonic regression problems. If all regression coefficients are positive then the resulting function is nondecreasing.

Value

XsplineBasis returns a matrix formed by the spline basis expansion of x.

knots(Fn) returns the knots attribute of Fn, which might be useful in a second call to the basis expansion function.

Author(s)

Steven L. Scott

References

Bsplines are described in deBoor (2001), "A Practical Guide to Splines". Springer.

Msplines and Isplines are reviewed by Ramsay (1988), Statistical Science pp. 425-461.

Examples

# Plot the B-spline basis for x with knots determined by 3 quantiles.
x <- sort(rnorm(1000))
basis <- BsplineBasis(x, numknots=3)
par(mfrow=c(2,3))
for(i in 1:5) plot(x, basis[, i], type="l")

# Plot the I-spline basis for x with the same knots.
basis <- IsplineBasis(x, numknots=3)
par(mfrow=c(2,3))
for(i in 1:5) plot(x, basis[, i], type="l")

# Bring you own knots...
basis <- BsplineBasis(x, knots = quantile(x, c(.2, .5, .8, .9)))
par(mfrow=c(2,3))
for(i in 1:6) plot(x, basis[, i], type="l")

knots(basis)