FLiRTI {PFLR}

FLiRTI Regression Model

Description

Calculates functional regression that's interpretable using the FLiRTI method.

Usage

FLiRTI(
  Y,
  X,
  d,
  cons,
  domain,
  extra = list(Mf = 6:30, lambda = seq(5e-04, 100, length.out = 50))
)

Arguments

Y

Vector of length n, centred response.

X

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

d

Integer, degree of the B-spline basis functions.

cons

Divide subinterval into how many small ones.

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 containing parameters which have default values:

• Mf: Mf+1 is the number of knots for the B-spline basis functions that expand \beta(t), default is 6:30.

• lambda: Tuning parameter, default is seq(0.0005,100,length.out = 50).

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.

• 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.

• delta: Estimated cutoff point.

• OptM: Optimal number of B-spline knots selected by BIC.

• Optlambda: Optimal shrinkage parameter selected by BIC.

Examples

library(fda)
betaind = 1
snr  = 2
nsim = 200
n    = 50
p    = 21
Y = array(NA,c(n,nsim))
X = array(NA,c(n,p,nsim))
domain = c(0,1)
lambda = seq(0.0005,0.01,length.out = 10)
Mf = 6:13
extra=list(Mf=Mf,lambda=lambda)

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


fltyfit = FLiRTI(Y=Y[1:n,1],(X[1:n,,1]),d=3,cons=4,domain=domain,extra=extra)