fda.usc (version 1.2.3)

fregre.basis.cv: Cross-validation Functional Regression with scalar response using basis representation.

Description

Computes functional regression between functional explanatory variables and scalar response using basis representation. The function fregre.basis.cv() uses validation criterion defined by argument type.CV to estimate the number of basis elements and/or the penalized parameter (lambda) that best predicts the response.

Usage

fregre.basis.cv(fdataobj,y,basis.x=NULL,basis.b=NULL,
type.basis=NULL,lambda=0,Lfdobj=vec2Lfd(c(0,0),rtt),
type.CV=GCV.S,par.CV=list(trim=0),weights= rep(1,n),
verbose=FALSE,...)

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.

type.basis

A vector of character string which determines type of basis. By default "bspline". It is only used when basis.x or basis.b are a vector of number of basis considered.

lambda

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

Lfdobj

See eval.penalty.

type.CV

Type of cross-validation. By default generalized cross-validation GCV.S method.

par.CV

List of parameters for type.CV: trim, the alpha of the trimming and draw.

weights

weights

verbose

If TRUE information about the procedure is printed. Default is FALSE.

...

Further arguments passed to or from other methods.

Value

• Return:
• call
  The matched call.
• coefficients
  A named vector of coefficients
• residuals
  y minus fitted values.
• fitted.values
  Estimated scalar response.
• beta.est
  beta parameter estimated of class fd
• weights
  (only for weighted fits) the specified weights.
• df
  The residual degrees of freedom.
• r2
  Coefficient of determination.
• sr2
  Residual variance.
• H
  Hat matrix.
• y
  Scalar response.
• fdataobj
  Functional explanatory data of class fdata.
• x.fd
  Centered functional explanatory data of class fd.
• lambda.opt
  lambda value that minimizes CV or GCV method.
• gcv.opt
  Minimum value of CV or GCV method.
• basis.x.opt
  Basis used for functional explanatory data estimation fdata.
• basis.b.opt
  Basis used for for functional beta parameter estimation.
• a.est
  Intercept parameter estimated
• lm
  Return lm object.

Details

If basis = NULL creates 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. If basis.x is a vector of number of basis elements and basis.b=NULL, the function force the same number of elements in the basis of x and beta. If basis.x$type=``fourier'' and basis.b$type=``fourier'', the function decreases the number of fourier basis elements on the $min(k_{n1},k_{n2})$, where $k_{n1}$ and $k_{n2}$ are the number of basis element of basis.x and basis.b respectively.

References

Ramsay, James O. and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York. Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

See Also

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

Examples

data(tecator)
x<-tecator$absorp.fdata[1:129]
y=tecator$y$Fat[1:129]
b1<-c(15,21,31)
b2<-c(7,9)
res1=fregre.basis.cv(x,y,basis.x=b1)
res2=fregre.basis.cv(x,y,basis.x=b1,basis.b=b2)
res1$gcv
res2$gcv
l=2^(-4:10)
res3=fregre.basis.cv(x,y,basis.b=b1,type.basis="fourier",
lambda=l,type.CV=GCV.S,par.CV=list(trim=0.15))
res3$gcv