# iSpline

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##### I-Spline Basis for Polynomial Splines or its derivatives

This function generates the I-spline (integral of M-spline) basis matrix for a polynomial spline or its derivatives of given order..

##### Usage
iSpline(x, df = NULL, knots = NULL, degree = 3L, intercept = FALSE,
Boundary.knots = range(x, na.rm = TRUE), derivs = 0L, ...)
##### Arguments
x

The predictor variable. Missing values are allowed and will be returned as they were.

df

Degrees of freedom. One can specify df rather than knots, then the function chooses "df - degree" (minus one if there is an intercept) knots at suitable quantiles of x (which will ignore missing values). The default, NULL, corresponds to no inner knots, i.e., "degree - intercept".

knots

The internal breakpoints that define the spline. 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. See also Boundary.knots.

degree

Non-negative integer degree of the piecewise polynomial. The default value is 3 for cubic splines. Note that the degree of I-spline is defined to be the degree of the associated M-spline instead of actual polynomial degree. In other words, I-spline basis of degree 2 is defined as the integral of associated M-spline basis of degree 2.

intercept

If TRUE, an intercept is included in the basis; Default is FALSE.

Boundary.knots

Boundary points at which to anchor the I-spline basis. By default, they are the range of the non-NA data. If both knots and Boundary.knots are supplied, the basis parameters do not depend on x. Data can extend beyond Boundary.knots.

derivs

A non-negative integer specifying the order of derivatives of I-splines.

...

Optional arguments for future usage.

##### Details

It is an implementation of the close form I-spline basis based on the recursion formula of B-spline basis. Internally, it calls mSpline and bSpline, and generates a basis matrix for representing the family of piecewise polynomials and their corresponding integrals with the specified interior knots and degree, evaluated at the values of x.

##### Value

A matrix of dimension length(x) by df = degree + length(knots) (plus on if intercept is included). Attributes that correspond to the arguments specified are returned for usage of other functions in this package.

##### References

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical science, 3(4), 425--441.

predict.iSpline for evaluation at given (new) values; deriv.iSpline for derivative method; mSpline for M-splines; cSpline for C-splines;

• iSpline
##### Examples
# NOT RUN {
## Example given in the reference paper by Ramsay (1988)
library(splines2)
x <- seq.int(0, 1, by = 0.01)
knots <- c(0.3, 0.5, 0.6)
isMat <- iSpline(x, knots = knots, degree = 2, intercept = TRUE)

library(graphics)
matplot(x, isMat, type = "l", ylab = "I-spline basis")
abline(v = knots, lty = 2, col = "gray")

## the derivative of I-splines is M-spline
msMat1 <- iSpline(x, knots = knots, degree = 2, derivs = 1)
msMat2 <- mSpline(x, knots = knots, degree = 2)
stopifnot(all.equal(msMat1, msMat2))
# }

Documentation reproduced from package splines2, version 0.2.5, License: GPL (>= 3)

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