Generates the I-spline (integral of M-spline) basis matrix for a polynomial spline or the corresponding derivatives of given order.
iSpline( x, df = NULL, knots = NULL, degree = 3L, intercept = TRUE, Boundary.knots = NULL, derivs = 0L, ... )
The predictor variable. Missing values are allowed and will be returned as they are.
Degree of freedom that equals to the column number of returned
matrix. One can specify
The internal breakpoints that define the spline. The default
The degree of I-spline defined to be the degree of the associated M-spline instead of actual polynomial degree. For example, I-spline basis of degree 2 is defined as the integral of associated M-spline basis of degree 2.
Boundary points at which to anchor the spline basis.
By default, they are the range of the non-
A non-negative integer specifying the order of derivatives of I-splines.
Optional arguments that are not used.
A numeric matrix with
length(x) rows and
df columns if
df is specified or
length(knots) + degree +
as.integer(intercept) columns if
knots are specified instead.
Attributes that correspond to the arguments specified are returned for
usage of other functions in this package.
It is an implementation of the close form I-spline basis based on the recursion formula given by Ramsay (1988).
Ramsay, J. O. (1988). Monotone regression splines in action. Statistical science, 3(4), 425--441.
library(splines2) ## Example given in the reference paper by Ramsay (1988) x <- seq.int(0, 1, by = 0.01) knots <- c(0.3, 0.5, 0.6) isMat <- iSpline(x, knots = knots, degree = 2) par(mar = c(2.5, 2.5, 0.2, 0.1), mgp = c(1.5, 0.5, 0)) matplot(x, isMat, type = "l", ylab = "I-spline basis")abline(v = knots, lty = 2, col = "gray")