Fitting Functional Generalized Linear Models
Computes functional generalized linear model between functional covariate X_j(t) (and non functional covariate Z_j) and scalar response Y using basis representation.
fregre.glm( formula, family = gaussian(), data, basis.x = NULL, basis.b = NULL, CV = FALSE, subset = NULL, ... )
formula |
an object of class |
family |
a description of the error distribution and link function to
be used in the model. This can be a character string naming a family
function, a family function or the result of a call to a family function.
(See |
data |
List that containing the variables in the model. |
basis.x |
List of basis for functional explanatory data estimation. |
basis.b |
List of basis for β(t) parameter estimation. |
CV |
=TRUE, Cross-validation (CV) is done . |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
... |
Further arguments passed to or from other methods. |
This function is an extension of the linear regression models:
fregre.lm where the E[Y|X,Z] is related to the linear
prediction η via a link function g(.).
E[Y|X,Z]= η = g^{-1}(α + ∑ β_j Z_j+∑ < X_k(t) , β_k(t) >)
where Z = [Z_1 ,..., Z_p] are the non functional covariates and X(t) = [ X_1(t_1) ,..., X_q(t_q)] are the functional ones.
The first item in the data list is called "df" and is a data
frame with the response and non functional explanatory variables, as
glm.
Functional covariates of class fdata or fd are introduced in
the following items in the data list.basis.x is a list of
basis for represent each functional covariate. The basis object can be
created by the function: create.pc.basis, pca.fd
create.pc.basis, create.fdata.basis o
create.basis.basis.b is a list of basis for
represent each β(t) parameter. If basis.x is a list of
functional principal components basis (see create.pc.basis or
pca.fd) the argument basis.b is ignored.
represent beta lower than the number of basis used to represent the functional data.
Return glm object plus:
basis.x Basis used for fdata or fd covariates.
basis.b Basis used for beta parameter estimation.
beta.l List of estimated beta parameter of functional covariates.
data List that containing the variables in the model.
formula formula.
CV predicted response by cross-validation.
If the formula only contains a non functional explanatory variables
(multivariate covariates), the function compute a standard glm
procedure.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.
McCullagh and Nelder (1989), Generalized Linear Models 2nd ed. Chapman and Hall.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S, New York: Springer.
See Also as: predict.fregre.glm and
summary.glm.
Alternative method if
family=gaussian: fregre.lm.
## Not run:
data(tecator)
x=tecator$absorp.fdata
y=tecator$y$Fat
tt=x[["argvals"]]
dataf=as.data.frame(tecator$y)
nbasis.x=11
nbasis.b=7
basis1=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.x)
basis2=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.b)
f=Fat~Protein+x
basis.x=list("x"=basis1)
basis.b=list("x"=basis2)
ldata=list("df"=dataf,"x"=x)
res=fregre.glm(f,family=gaussian(),data=ldata,basis.x=basis.x,
basis.b=basis.b)
summary(res)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.