SLoS {PFLR}

SLoS regression Model

Description

Calculates functional regression using the Smooth and Locally Sparse (SLoS) method.

Usage

SLoS(
  Y,
  X,
  M,
  d,
  domain,
  extra = list(Maxiter = 100, lambda = exp(seq(-30, 0, length.out = 10)), gamma =
    10^(-10:10), absTol = 10^(-10), Cutoff = 10^(-6))
)

Arguments

Y

Vector, length n, centred response.

X

Matrix of n x p, covariate matrix, should be dense, centred.

M

Integer, t1,..., tM are M equally spaced knots.

d

Integer, the degree of B-Splines.

domain

The range over which the function X(t) is evaluated and the coefficient function \beta(t) is expanded by the B-spline basis functions.

extra

List of parameters which have default values:

• Maxiter: Maximum number of iterations for convergence of beta, default is 100.

• lambda: Positive number, tuning parameter for fSCAD penalty, default is exp(seq(-30,0, length.out = 10)).

• gamma: Positive number, tuning parameter for the roughness penalty, default is 10^(-10:10).

• absTol: Number, if max(norm(bHat)) is smaller than absTol, we stop another iteration, default is 10^(-10).

• Cutoff: Number, if bHat is smaller than Cutoff, set it to zero to avoid being numerically unstable, default is 10^(-6).

Value

beta: Estimated \beta(t) at discrete points.

extra: List containing other values which may be of use:

• X: Matrix of n x p used for model.

• Y: Vector of length n used for model.

• M: Integer representing the number of knots used in the model calculation.

• d: Integer, degree of B-Splines used.

• domain: The range over which the function X(t) was evaluated and the coefficient function \beta(t) was expanded by the B-spline basis functions.

• b: Estimated b values.

• delta: Estimated cutoff point.

• Optgamma: Optimal smoothing parameter selected by BIC.

• Optlambda: Optimal shrinkage parameter selected by BIC.

Examples

library(fda)
betaind = 1
snr  = 2
nsim = 1
n    = 50
p    = 21
Y = array(NA,c(n,nsim))
X = array(NA,c(n,p,nsim))
domain = c(0,1)

M = 20
d = 3
norder   = d+1
nknots   = M+1
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = fda::create.bspline.basis(knots,nbasis,norder)
V = eval.penalty(basis,int2Lfd(2))

extra=list(lambda=exp(seq(-18,-12, length.out = 10)),gamma=10^(-8:-6))

for(itersim in 1:nsim)
{
 dat = ngr.data.generator.bsplines(n=n,nknots=64,norder=4,p=p,domain=domain,snr=snr,betaind=betaind)
  Y[,itersim]  = dat$Y
  X[,,itersim] = dat$X
}

slosfit = SLoS(Y=Y[1:n,1],(X[1:n,,1]),M=M,d=d,domain=domain,extra=extra)