Package 'PFLR' reference manual

Title:	Estimating Penalized Functional Linear Regression
Description:	Implementation of commonly used penalized functional linear regression models, including the Smooth and Locally Sparse (SLoS) method by Lin et al. (2016) <doi:10.1080/10618600.2016.1195273>, Nested Group bridge Regression (NGR) method by Guan et al. (2020) <doi:10.1080/10618600.2020.1713797>, Functional Linear Regression That's interpretable (FLIRTI) by James et al. (2009) <doi:10.1214/08-AOS641>, and the Penalized B-spline regression method.
Authors:	Tianyu Guan [aut], Haolun Shi [aut, cre, cph], Rob Cameron [aut], Zhenhua Lin [aut]
Maintainer:	Haolun Shi <[email protected]>
License:	GPL-2
Version:	1.1.0
Built:	2025-02-19 03:28:34 UTC
Source:	https://github.com/cran/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))
)
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)


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)

Nested Group Bridge Regression Model

Description

Calculates a functional regression model using a nested group bridge approach.

Usage

ngr(
  Y,
  X,
  M,
  d,
  domain,
  extra = list(alphaPS = 10^(-10:0), kappa = 10^(-(9:7)), tau = exp(seq(-50, -15, len =
    20)), gamma = 0.5, niter = 100)
)
ngr(
  Y,
  X,
  M,
  d,
  domain,
  extra = list(alphaPS = 10^(-10:0), kappa = 10^(-(9:7)), tau = exp(seq(-50, -15, len =
    20)), gamma = 0.5, niter = 100)
)

Arguments

`Y`	Vector of length n.
`X`	Matrix of n x p, covariate matrix, should be dense.
`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 containing other parameters which have defaults: alphaPs: Smoothing parameter for the Penalized B-splines method, default is 10^(-10:0). kappa: Tuning parameter for roughness penalty, default is 10^(-(9:7)). tau: Tuning parameter for the group bridge penalty, default is exp(seq(-50,-15,len = 20)). gamma: Real number, default is 0.5. niter: Integer, maximum number of iterations, default is 100.

Value

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

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

b: Estimated b-hat.
delta: Estimated cutoff point.
Ymean: Estimated y-hat.
Xmean: Estimated x-hat.
Optkappa: Optimal roughness penalty selected.
Opttau: Optimal group bridge penalty selected.
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.

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis)
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis)
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

Generating random curves from B-Splines

Description

Generating random curves from B-Splines n,nknots,norder,p,domain=c(0,1),snr,betaind

Usage

ngr.data.generator.bsplines(
  n,
  nknots,
  norder,
  p,
  domain = c(0, 1),
  snr,
  betaind
)
ngr.data.generator.bsplines(
  n,
  nknots,
  norder,
  p,
  domain = c(0, 1),
  snr,
  betaind
)

Arguments

`n`	Number of curves
`nknots`	Number of knots
`norder`	Degree
`p`	Number of time points
`domain`	Domain of time
`snr`	Signal to noise ratio
`betaind`	Numeric index for function

Value

X: The generated X matrix of curve sampled at each timepoint

Y: The generated dependent variable

Penalized B-splines Regression Model

Description

Calculates a functional regression model using the penalized B-splines method.

Usage

PenS(Y, X, alpha, M, d, domain)
PenS(Y, X, alpha, M, d, domain)

Arguments

`Y`	Vector of length n.
`X`	Matrix of n x p, covariate matrix, should be dense.
`alpha`	Vector.
`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.

Value

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

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

b: Estimated B-spline coefficients.
Ymean: Mean of the Y values.
Xmean: Mean of all X values.
Optalpha: Optimal alpha value chosen.
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.

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)



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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

Plot Method for flirti Objects

Description

Plots coefficient function of objects of class "flirti".

Usage

## S3 method for class 'flirti'
plot(x, ...)
## S3 method for class 'flirti'
plot(x, ...)

Arguments

`x`	An object of class "flirti".
`...`	Other parameters to be passed through to plotting functions.

Value

A line graph of the beta values versus time.

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)

plot(fltyfit)

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)

plot(fltyfit)

Plot Method for ngr Objects

Description

Plots coefficient function for objects of the class "ngr".

Usage

## S3 method for class 'ngr'
plot(x, ...)
## S3 method for class 'ngr'
plot(x, ...)

Arguments

`x`	An object of class "ngr".
`...`	Other parameters to be passed through to plotting functions.

Value

A line graph of the beta values over time.

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

plot(ngrfit)

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

plot(ngrfit)

Plot Method for Penalized B-splines Objects

Description

Plots coefficient function of objects of class "ps".

Usage

## S3 method for class 'ps'
plot(x, ...)
## S3 method for class 'ps'
plot(x, ...)

Arguments

`x`	An object of class "ps".
`...`	Other parameters to be passed through to plotting functions.

Value

A line graph of the beta values versus time.

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

plot(psfit)

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

plot(psfit)

Plot Method for SLoS Objects

Description

Plots coefficient function for objects of class "slos".

Usage

## S3 method for class 'slos'
plot(x, ...)
## S3 method for class 'slos'
plot(x, ...)

Arguments

`x`	An object of class "slos".
`...`	Other parameters to be passed through to plotting functions.

Value

A line graph of the beta values versus time.

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    = 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)
plot(slosfit)


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    = 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)
plot(slosfit)

Predict Method for flirti Objects

Description

Predicted values based on objects of the class "flirti".

Usage

## S3 method for class 'flirti'
predict(object, Xnew, ...)
## S3 method for class 'flirti'
predict(object, Xnew, ...)

Arguments

`object`	An object of class "flirti".
`Xnew`	New covariate matrix for prediction, should be dense, centred.
`...`	Not applicable

Value

Predicted values.

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)

predict(fltyfit,(X[1:n,,1]))


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)

predict(fltyfit,(X[1:n,,1]))

Predict Method for ngr Objects

Description

Predicted values based on "ngr" class objects.

Usage

## S3 method for class 'ngr'
predict(object, Xnew, ...)
## S3 method for class 'ngr'
predict(object, Xnew, ...)

Arguments

`object`	An object of class "ngr".
`Xnew`	New covariate matrix for prediction, should be dense, centred.
`...`	Not applicable

Value

Estimated Y hat value.

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))
predict(ngrfit,X[1:n,,1])

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))
predict(ngrfit,X[1:n,,1])

Predict Method for Penalized B-splines objects

Description

Predicted values based on objects of class "ps".

Usage

## S3 method for class 'ps'
predict(object, Xnew, ...)
## S3 method for class 'ps'
predict(object, Xnew, ...)

Arguments

`object`	An object of class "ps".
`Xnew`	New covariate matrix for prediction, should be dense, centred.
`...`	Not applicable

Value

Predicted values.

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

predict(psfit,X[1:n,,1])

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

predict(psfit,X[1:n,,1])

Predict Method for SLoS objects

Description

Predicted values based on objects of class "slos".

Usage

## S3 method for class 'slos'
predict(object, Xnew, ...)
## S3 method for class 'slos'
predict(object, Xnew, ...)

Arguments

`object`	An object of class "slos".
`Xnew`	New covariate matrix for prediction, should be dense, centred.
`...`	Not applicable

Value

Predicted values.

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    = 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)

predict(slosfit,(X[1:n,,1]))

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    = 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)

predict(slosfit,(X[1:n,,1]))

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(-20, -12, length.out = 10)), gamma =
    10^(-9:0), absTol = 10^(-10), Cutoff = 10^(-6))
)
SLoS(
  Y,
  X,
  M,
  d,
  domain,
  extra = list(Maxiter = 100, lambda = exp(seq(-20, -12, length.out = 10)), gamma =
    10^(-9:0), 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(-20,-12, length.out = 10)). gamma: Positive number, tuning parameter for the roughness penalty, default is 10^(-9:0). 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)


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)

Summary Method for flirti Objects

Description

Summarizes the values of an object of class "flirti".

Usage

## S3 method for class 'flirti'
summary(object, ...)
## S3 method for class 'flirti'
summary(object, ...)

Arguments

`object`	An object of class "flirti".
`...`	Not applicable

Value

Prints a 5 number summary of the beta values, delta, OptM, and Optlambda

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)

summary(fltyfit)


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)

summary(fltyfit)

Summary Method for ngr Objects

Description

Summarizes objects of class "ngr".

Usage

## S3 method for class 'ngr'
summary(object, ...)
## S3 method for class 'ngr'
summary(object, ...)

Arguments

`object`	An object of class "ngr".
`...`	Not applicable

Value

Prints the 5 number summaries of beta and b values. Prints delta, Optkappa, and Opttau values.

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

summary(ngrfit)

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
tobs = seq(domain[1],domain[2],length.out = p)
knots    = seq(domain[1],domain[2],length.out = nknots)
nbasis   = nknots + norder - 2
basis    = create.bspline.basis(knots,nbasis,norder)
basismat = eval.basis(tobs, basis) 
h = (domain[2]-domain[1])/M
cef = c(1, rep(c(4,2), (M-2)/2), 4, 1)

V = eval.penalty(basis,int2Lfd(2))
alphaPS = 10^(-(10:3))
kappa   = 10^(-(8:7))
tau     = exp(seq(-35,-28,len=20))
gamma   = 0.5


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
}

ngrfit = ngr(Y=Y[1:n,1],X=(X[1:n,,1]),M,d,domain,extra= list(alphaPS=alphaPS, kappa=kappa, tau=tau))

summary(ngrfit)

Summary Method for Penalized B-splines Objects

Description

Summarizes the values of an object of class "ps".

Usage

## S3 method for class 'ps'
summary(object, ...)
## S3 method for class 'ps'
summary(object, ...)

Arguments

`object`	An object of class "ps".
`...`	Not applicable

Value

Prints a 5 number summary of the beta values and coefficient values, and the optimal alpha.

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

summary(psfit)

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
alpha = 10^(-(10:3))


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
}

psfit = PenS(Y=Y[1:n,1],X=(X[1:n,,1]), alpha=alpha, M=M, d=d, domain=domain)

summary(psfit)

Summary Method for SLoS Objects

Description

Summarizes values of an object of class "slos".

Usage

## S3 method for class 'slos'
summary(object, ...)
## S3 method for class 'slos'
summary(object, ...)

Arguments

`object`	An object of class "slos".
`...`	Not applicable

Value

Prints five number summary of beta values, delta, Optgamma, and Optlambda.

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    = 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)

summary(slosfit)


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    = 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)

summary(slosfit)

The particulate matter emissions data, taken from the Coordinating Research Councils E55/E59 research project (Clark et al. 2007). In the project, trucks were placed on the chassis dynamometer bed to mimic inertia and particulate matter was measured by an emission analyzer on standard test cycles. The engine acceleration of diesel trucks was also recorded.

Usage

truck
truck

Format

A data frame with 108 rows and 91 columns:

Y: Emmission
X1-X90: Acceleration at each second

Source

Clark, N., Gautam, M., Wayne, W., Lyons, D., Thompson, G., and Zielinska, B. (2007), “Heavy-Duty Vehicle Chassis Dynamometer Testing for Emissions Inventory, Air Quality Modeling, Source Apportionment and Air Toxics Emissions Inventory: E55/59 All Phases,” Coordinating Research Council, Alpharetta

Package 'PFLR'

Help Index

FLiRTI Regression Model

Description

Usage

Arguments

Value

Examples

Nested Group Bridge Regression Model

Description

Usage

Arguments

Value

Examples

Generating random curves from B-Splines

Description

Usage

Arguments

Value

Penalized B-splines Regression Model

Description

Usage

Arguments

Value

Examples

Plot Method for flirti Objects

Description

Usage

Arguments

Value

Examples

Plot Method for ngr Objects

Description

Usage

Arguments

Value

Examples

Plot Method for Penalized B-splines Objects

Description

Usage

Arguments

Value

Examples

Plot Method for SLoS Objects

Description

Usage

Arguments

Value

Examples

Predict Method for flirti Objects

Description

Usage

Arguments

Value

Examples

Predict Method for ngr Objects

Description

Usage

Arguments

Value

Examples

Predict Method for Penalized B-splines objects

Description

Usage

Arguments

Value

Examples

Predict Method for SLoS objects

Description

Usage

Arguments

Value

Examples

SLoS regression Model

Description

Usage

Arguments

Value

Examples

Summary Method for flirti Objects