fda.usc (version 0.9.4)

fregre.pc: Functional Regression with scalar response using Principal Components Analysis.

Description

Computes functional regression between functional explanatory variables and scalar response using Principal Components Analysis.

Usage

fregre.pc(fdataobj,y,l=1:3,norm=TRUE)

Arguments

fdataobj

fdata class object.

y

Scalar response with length n.

l

Vector of principal comoponents.

norm

=TRUE the norm of eigenvectors (rotation) is 1.

Value

• Return:
• call
  The matched call of fregre.pc function.
• beta.est
  beta coefficient estimated of class fdata
• coefficients
  A named vector of coefficients.
• fitted.values
  Estimated scalar response.
• lambda
  Eigenvalues of the covariance/correlation matrix.
• vs
  A matrix whose columns contain the eigenvectors selected by l index.
• Z
  Matrix of centered fdata multiplied by the eigenvalues vs.
• H
  Hat matrix.
• df
  The residual degrees of freedom.
• residuals
  y-fitted values.
• r2
  Coefficient of determination.
• sr2
  Residual variance.
• fdataobj
  Functional explanatory data.
• y
  Scalar response.
• pf
  Formula used in lm function
• pc
  pc.svd.fdata object.
• l
  Index of principal components selected.
• lm
  lm object.

Details

The principal components are calculated by svd decomposition in the pc.svd.fdata function.

References

Cai TT, Hall P. 2006. Prediction in functional linear regression. Annals of Statistics 34: 2159{-}2179. Cardot H, Ferraty F, Sarda P. 1999. Functional linear model. Statistics and Probability Letters 45: 11{-}22. Hall P, Hosseini{-}Nasab M. 2006. On properties of functional principal components analysis. Journal of the Royal Statistical Society B 68: 109{-}126.

See Also

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

Examples

data(tecator)
absorp=tecator$absorp.fdata
ind=1:129
x=absorp[ind,]
y=tecator$y$Fat[ind]

res=fregre.pc(x,y)
summary(res)
pc.cor(x,y,1:8)
pc.fdata(x,1:8,draw=FALSE)
res2=fregre.pc(x,y,l=c(1,3,4))
summary(res2)
x.d=fdata.deriv(x)
pc.cor(x.d,y,1:8)
pc.fdata(x.d,1:8,draw=FALSE)
res3=fregre.pc(x.d,y,l=c(1,3,4))
summary(res3)