This function fits iteratively a functional linear model using generalized least squares. The errors are allowed to be correlated and/or have unequal variances.
Begin with a preliminary estimation of \(\hat{\theta}=\theta_0\) (for instance, \(\theta_0=0\)). Compute \(\hat{W}\).
Estimate \(b_\Sigma =(Z'\hat{W}Z)^{-1}Z'\hat{W}y\)
Based on the residuals, \(\hat{e}=\left(y-Zb_\Sigma \right)\), update \(\hat{\theta}=\rho\left({\hat{e}}\right)\) where \(\rho\) depends on the dependence structure chosen.
Repeats steps 2 and 3 until convergence (small changes in \(b_\Sigma\) and/or \(\hat{\theta}\)).
fregre.igls(
formula,
data,
basis.x = NULL,
basis.b = NULL,
correlation,
maxit = 100,
rn,
lambda,
weights = rep(1, n),
control,
...
)
A two-sided linear formula object describing the
model, with the response on the left of a ~
operator and the
terms, separated by +
operators, on the right.
An optional data frame containing the variables named in
model
, correlation
, weights
, and
subset
. By default the variables are taken from the environment
from which gls
is called.
List of basis for functional explanatory data estimation.
List of basis for \(\beta(t)\) parameter estimation.
an optional corStruct
object describing the
within-group correlation structure. See the documentation of
corClasses
for a description of the available corStruct
classes. If a grouping variable is to be used, it must be specified in
the form
argument to the corStruct
constructor. Defaults to
NULL
, corresponding to uncorrelated errors.
Number of maximum of interactions.
List of Ridge parameter.
List of Roughness penalty parameter.
An optional varFunc
object or one-sided formula
describing the within-group heteroscedasticity structure. If given as
a formula, it is used as the argument to varFixed
,
corresponding to fixed variance weights. See the documentation on
varClasses
for a description of the available varFunc
classes. Defaults to NULL
, corresponding to homoscedastic errors.
Control parameters.
Further arguments passed to or from other methods.
An object of class "gls"
representing the functional linear model
fit. Generic functions such as print
, plot
, and summary
have
methods to show the results of the fit.
See glsObject
for the components of the fit. The functions
resid
, coef
and fitted
, can be used to
extract some of its components.
Beside, the class(z) is "gls", "lm" and "fregre.lm" with the following objects:
sr2 Residual variance.
Vp Estimated covariance matrix for the parameters.
lambda A roughness penalty.
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 used in ajusted model.
formula.ini formula in call.
XX desing matrix
W inverse of covariance matrix
fdataob
rn rn
vs.list
correlation See glsObject for the components of the fit.
Oviedo de la Fuente, M., Febrero-Bande, M., Pilar Munoz, and Dominguez, A. Predicting seasonal influenza transmission using Functional Regression Models with Temporal Dependence. arXiv:1610.08718. https://arxiv.org/abs/1610.08718
# NOT RUN {
data(tecator)
x=tecator$absorp.fdata
x.d2<-fdata.deriv(x,nderiv=)
tt<-x[["argvals"]]
dataf=as.data.frame(tecator$y)
# plot the response
plot(ts(tecator$y$Fat))
ldata=list("df"=dataf,"x.d2"=x.d2)
res.gls=fregre.igls(Fat~x.d2,data=ldata,
correlation=list("cor.ARMA"=list()),
control=list("p"=1))
res.gls
res.gls$corStruct
# }
Run the code above in your browser using DataLab