tp: Generate basis functions for penalized spline smoothing.

Description

tp generates a truncated power basis and bsp generates a reparameterized b-spline basis for penalized spline smoothing.

Usage

tp(x, degree=1, k=15, by=NULL, allPen=FALSE, varying=NULL, diag=FALSE,
    knots=quantile(x, probs = (1:(k - degree))/(k - degree  + 1)), 
    centerscale=NULL, scaledknots=FALSE)
    
bsp(x, k=15, spline.degree=3, diff.ord=2, knots, by,
    allPen=FALSE, varying, diag=FALSE)

Arguments

covariate for the smooth function

degree

integer: degree of truncated polynomials (0: piecewise constant, 1: piecewise linear etc..)

integer: dimensionality of the basis (i.e.: number of knots + degree)

factor variable: estimate separate functions for each level - this assumes standard treatment contrasts for the supplied factor.

allPen

boolean: if TRUE, make design for group-specific curves with common smoothing parameter: all parameters (including the normally unpenalized basis functions in X) are penalized, every level of "by" has the same amount of smoothing if FALSE, make design fo

varying

numeric: if not NULL, a varying coefficient model is fit: f(x,varying) = f(x)*varying

diag

logical: force a diagonal covariance-matrix for the random effects for X if allPen=TRUE?

knots

vector of knot locations (optional). Defaults to quantile-based knots at the $i/(k+1-$degree)-quantiles for $i=1,\dots,k-$degree.

centerscale

numeric(2): center&scale x by these values if not NULL

scaledknots

boolean: are knot locations given for the rescaled x-values?

spline.degree

integer: degree of B-splines (defaults to cubic)

diff.ord

integer: order of the difference penalty on the un-reparamerized spline coefficients. Defaults to 2, that is, penalized deviations from linearity.

Value

list with entries: "X": For tp, it is an n x degree design matrix for unpenalized part (without intercept) (or a list of those for every level of by if allPen=F); and for bsp, it is an n x (diff.ord - 1) design matrix for unpenalized part (without intercept).
"Z": For tp, it is an n x (k-degree) design matrix for penalized part (or a list of those for every level of by if allPen=F); and for bsp, it is an n x (k - diff.ord+1) design matrix for penalized part.

Details

tp generates truncated power bases which have degree unpenalized basis functions, namely $x^1,\dots, x^{degree}$ and $k-$degree penalized basis functions that contain the positive part $(x-\kappa_j)^{degree}$ for knots $\kappa_j, j=1,dots,k-$degree. This function can be used as a reference when implementing other basisGenerators that can be used for additive models through cpglmm.

bsp generate a b-spline basis with equidistant knots in mixed model reparameterization.