fda.usc (version 0.9.4)

fregre.basis: Functional Regression with scalar response using basis representation.

Description

Computes functional regression between functional explanatory variable and scalar response using basis representation.

Usage

fregre.basis(fdataobj,y,basis.x=NULL,basis.b=NULL,
lambda=0,Lfdobj=vec2Lfd(c(0,0),rtt),...)

Arguments

fdataobj

fdata class object.

y

Scalar response with length n.

basis.x

Basis for functional explanatory data fdataobj.

basis.b

Basis for functional beta parameter.

lambda

A roughness penalty. By default, no penalty lambda=0.

Lfdobj

See eval.penalty.

...

Further arguments passed to or from other methods.

Value

• Return:
• call
  The matched call.
• beta.est
  beta coefficient estimated of class fd
• a.est
  Intercept parameter estimated
• fitted.values
  Estimated scalar response.
• H
  Hat matrix.
• residuals
  y minus fitted values.
• df
  The residual degrees of freedom.
• r2
  Coefficient of determination.
• sr2
  Residual variance.
• y
  Response.
• fdataobj
  Functional explanatory data of class fdata.
• basis.b
  Basis used for beta parameter estimation.
• lm
  Return lm object

Details

If basis=NULL creates the bspline basis. If the functional covariate fdataobj is in a format "raw data", such as matrix or data.frame, creates an object of class "fdata" with default attributes, see fdata.

References

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

See Also

See Also as: fregre.basis.cv, summary.fregre.fd and predict.fregre.fd. Alternative method: fregre.pc and fregre.np.

Examples

# fregre.basis
data(tecator)
names(tecator)
absorp=tecator$absorp.fdata
ind=1:129
x=absorp[ind,]
y=tecator$y$Fat[ind]
tt=absorp[["argvals"]]


res1=fregre.basis(x,y)
summary(res1)
basis1=create.bspline.basis(rangeval=range(tt),nbasis=19)
basis2=create.bspline.basis(rangeval=range(tt),nbasis=9)
res5=fregre.basis(x,y,basis1,basis2)
summary(res5)
x.d2=fdata.deriv(x,nbasis=19,nderiv=1,method="bspline",class.out="fdata")
res7=fregre.basis(x.d2,y,basis1,basis2)
summary(res7)