psp function

Tool to build the basis matrix and the penalty matrix of P-splines.

psp builds the basis matrix and the penalty matrix to approximate a smooth function using a P-spline.

psp(xx, lambda, b.order, nknots, diff)

Arguments

• xx: the explanatory variable.
• lambda: an optional positive value that represents the smoothing parameter value.
• b.order: an optional positive integer that specifies the degree of the B-spline basis matrix. Default is 3.
• nknots: an optional positive integer that represents the number of internal knots of the P-spline. Default is $m=[n^{\frac{1}{3}}]+3$. The knots are located at the quantiles of order $0/(m-1),1/(m-1),\ldots,(m-1)/(m-1)$ of xx.
• diff: an optional positive integer that specifies the order of the difference penalty term. Default is 2.

Returns

• xx: the explanatory variable $xx$ with the following attributes: set of knots, B-spline basis matrix, penalty matrix and smoothing parameter (if it was specified).

References

Eilers P.H.C. and Marx B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science. 11, 89-121.

Author(s)

Luis Hernando Vanegas hvanegasp@gmail.com and Gilberto A. Paula

Examples

n <- 300
t <- sort(round(runif(n),digits=2))

t2 <- psp(t, diff=3)
N <- attr(t2, "N") ## B-spline basis matrix
M <- attr(t2, "K") ## Penalty Matrix
knots <- attr(t2,"knots") ## Set of knots