Fit Functional Linear Model Using Generalized Least Squares

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

Usage

fregre.gls(
  formula,
  data,
  correlation = NULL,
  basis.x = NULL,
  basis.b = NULL,
  rn,
  lambda,
  weights = NULL,
  subset,
  method = c("REML", "ML"),
  control = list(),
  verbose = FALSE,
  criteria = "GCCV1",
  ...
)

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.
correlation: 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.
basis.x: List of basis for functional explanatory data estimation.
basis.b: List of basis for \(\beta(t)\) parameter estimation.
rn: List of Ridge parameter.
lambda: List of Roughness penalty parameter.
weights: 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.
subset: an optional expression indicating which subset of the rows of data should be used in the fit. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.
method: a character string. If "REML" the model is fit by maximizing the restricted log-likelihood. If "ML" the log-likelihood is maximized. Defaults to "REML".
control: a list of control values for the estimation algorithm to replace the default values returned by the function glsControl. Defaults to an empty list.
verbose: an optional logical value. If TRUE information on the evolution of the iterative algorithm is printed. Default is FALSE.
criteria: GCCV criteria, see GCCV.S.
...: some methods for this generic require additional arguments. None are used in this method.

Value

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.
Besides, 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 containing the variables in the model.
formula: Formula used in the adjusted model.
formula.ini: Formula in call.
W: Inverse of covariance matrix.
correlation: See glsObject for the components of the fit.

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

if (FALSE) { # \dontrun{ 
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))

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)
basis.x=list("x.d2"=basis1)
basis.b=list("x.d2"=basis2)
ldata=list("df"=dataf,"x.d2"=x.d2)
res.gls=fregre.gls(Fat~x.d2,data=ldata, correlation=corAR1(),
                   basis.x=basis.x,basis.b=basis.b)
summary(res.gls)                   
} # }