fda.usc (version 2.1.0)

fregre.igls: Fit of Functional Generalized Least Squares Model Iteratively

Description

This function fits iteratively a functional linear model using generalized least squares. The errors are allowed to be correlated and/or have unequal variances.

1. Begin with a preliminary estimation of \(\hat{\theta}=\theta_0\) (for instance, \(\theta_0=0\)). Compute \(\hat{W}\).

2. Estimate \(b_\Sigma =(Z'\hat{W}Z)^{-1}Z'\hat{W}y\)

3. 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.

4. Repeats steps 2 and 3 until convergence (small changes in \(b_\Sigma\) and/or \(\hat{\theta}\)).

Usage

fregre.igls(
  formula,
  data,
  basis.x = NULL,
  basis.b = NULL,
  correlation,
  maxit = 100,
  rn,
  lambda,
  weights = rep(1, n),
  control,
  ...
)

Value

An object of class "fregre.igls" representing the functional linear model fit with temporal dependence errors. Beside, the class(z) is similar to "fregre.lm" plus the following objects:

• corStruct Fitted AR or ARIMA model.

Arguments

formula

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.

data

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.

basis.x

List of basis for functional explanatory data estimation.

basis.b

List of basis for \(\beta(t)\) parameter estimation.

correlation

List describing the correlation structure. Defaults to NULL, corresponding to uncorrelated errors. See the following internal functions for a description and a code example in script file.

• corUnstruc(x), fit an unstrutured correlation.

• cor.AR(x, order.max = 8, p=1, method = "lm") fit an Autoregressive Models to Time Series using ar function.

• cor.ARMA(x, p, d = 0, q = 0, method = "lm", order.max = 1) Fit an ARIMA model to a univariate time series using arima function.

• corExpo(xy,range, method = "euclidean",p=2) Fit an exponential correlation structure.

maxit

Number of maximum of interactions.

rn

List of Ridge parameter.

lambda

List of Roughness penalty parameter.

weights

weights

control

Control parameters.

...

Further arguments passed to or from other methods.

References

Oviedo de la Fuente, M., Febrero-Bande, M., Pilar Munoz, and Dominguez, A. (2018). Predicting seasonal influenza transmission using functional regression models with temporal dependence. PloS one, 13(4), e0194250. tools:::Rd_expr_doi("10.1371/journal.pone.0194250")

Examples

if (FALSE) { 
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
}