centeredBasis.gen: Generation of a recentered cubic B-spline basis matrix.

In tvcure: Additive Cure Survival Model with Time-Varying Covariates

Generation of a recentered cubic B-spline basis matrix.

Description

Generation of a cubic B-spline basis matrix with recentered columns to handle the identifiability constraint in additive models. See Wood (CRC Press 2017, pp. 175-176) for more details.

Usage

centeredBasis.gen(x, knots, cm = NULL, pen.order = 2)

Arguments

x	Vector of values where the "recentered" B-spline basis is evaluated.
knots	Vector of knots that must cover the values in x.
cm	(Optional) values subtracted from each column of the original B-spline matrix.
pen.order	Order of the penalty applied on B-spline parameters. (Default: 2).

Value

List containing

• B : centered cubic B-spline matrix obtained by subtracting cm[j] from the jth B-spline in column j of the original B-spline matrix evaluated at x.

• Dd : difference matrix (of order pen.order) for the associated centered B-spline matrix.

• Pd : penalty matrix (of order pen.order) for the associated centered B-spline matrix.

• K : number of centered B-splines in the basis.

• cm : values subtracted from each column of the original B-spline matrix. By default, this is a vector containing the mean of each column in the original B-spline matrix.

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. and Kreyenfeld, M. (2025). Time-varying exogenous covariates with frequently changing values in double additive cure survival model: an application to fertility. Journal of the Royal Statistical Society, Series A. <doi:10.1093/jrsssa/qnaf035>

Examples

x = seq(0,1,by=.01)
knots = seq(0,1,length=5)
obj = centeredBasis.gen(x,knots)
matplot(x,obj$B,type="l",ylab="Centered B-splines")
colMeans(obj$B)

tvcure documentation built on April 12, 2025, 1:58 a.m.