fda.usc (version 2.0.1)

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.

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

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.

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

# NOT RUN {
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
# }
# NOT RUN {
# }