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Generates basis matrix for integrals of B-splines.

## Usage

ibs(
x,
df = NULL,
knots = NULL,
degree = 3,
intercept = FALSE,
Boundary.knots = NULL,
...
)

## 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 than knots, then the function chooses df - degree - as.integer(intercept) internal knots at suitable quantiles of x ignoring missing values and those x outside of the boundary. If internal knots are specified via knots, the specified df 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 excluding NA. If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.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.

## Details

The implementation is based on the closed-form recursion formula.

## References

De Boor, Carl. (1978). A practical guide to splines. Vol. 27. New York: Springer-Verlag.

## See also

bSpline for B-splines; dbs for derivatives of B-splines;

## 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)