Generates basis matrix for integrals of B-splines.
Arguments
- x
The predictor variable. Missing values are allowed and will be returned as they are.
- df
Degree of freedom that equals to the column number of the returned matrix. One can specify
df
rather thanknots
, then the function choosesdf - degree - as.integer(intercept)
internal knots at suitable quantiles ofx
ignoring missing values and thosex
outside of the boundary. If internal knots are specified viaknots
, the specifieddf
will be ignored.- knots
The internal breakpoints that define the splines. The default is
NULL
, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots.- degree
A nonnegative integer specifying the degree of the piecewise polynomial. The default value is
3
for cubic splines. Zero degree is allowed for piecewise constant basis functions.- intercept
If
TRUE
, the complete basis matrix will be returned. Otherwise, the first basis will be excluded from the output.- Boundary.knots
Boundary points at which to anchor the splines. By default, they are the range of
x
excludingNA
. If bothknots
andBoundary.knots
are supplied, the basis parameters do not depend onx
. Data can extend beyondBoundary.knots
.- ...
Optional arguments that are not used.
Value
A numeric matrix of 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
mainly for other functions in this package.
Examples
library(splines2)
x <- seq.int(0, 1, 0.01)
knots <- c(0.2, 0.4, 0.7, 0.9)
ibsMat <- ibs(x, knots = knots, degree = 1, intercept = TRUE)
## get the corresponding B-splines by bSpline()
bsMat0 <- bSpline(x, knots = knots, degree = 1, intercept = TRUE)
## or by the deriv() method
bsMat <- deriv(ibsMat)
stopifnot(all.equal(bsMat0, bsMat, check.attributes = FALSE))
## plot B-spline basis with their corresponding integrals
op <- par(mfrow = c(1, 2))
matplot(x, bsMat, type = "l", ylab = "B-spline basis")
abline(v = knots, lty = 2, col = "gray")
matplot(x, ibsMat, type = "l", ylab = "Integral of B-spline basis")
abline(v = knots, lty = 2, col = "gray")
## reset to previous plotting settings
par(op)