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

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

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{θ}=θ_0 (for instance, θ_0=0). Compute \hat{W}.

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

3. Based on the residuals, \hat{e}=≤ft(y-Zb_Σ \right), update \hat{θ}=ρ≤ft({\hat{e}}\right) where ρ depends on the dependence structure chosen.

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

Usage

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

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 β(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.

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.

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. doi: 10.1371/journal.pone.0194250

Examples

## 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

## End(Not run)

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.