R: Penalized function-on-function regression with non-i.i.d....

pffrGLS {refund}

R Documentation

Penalized function-on-function regression with non-i.i.d. residuals

Description

Implements additive regression for functional and scalar covariates and functional responses. This function is a wrapper for mgcv's gam and its siblings to fit models of the general form
Y_i(t) = \mu(t) + \int X_i(s)\beta(s,t)ds + f(z_{1i}, t) + f(z_{2i}) + z_{3i} \beta_3(t) + \dots + E_i(t))
with a functional (but not necessarily continuous) response Y(t), (optional) smooth intercept \mu(t), (multiple) functional covariates X(t) and scalar covariates z_1, z_2, etc. The residual functions E_i(t) \sim GP(0, K(t,t')) are assumed to be i.i.d. realizations of a Gaussian process. An estimate of the covariance operator K(t,t') evaluated on yind has to be supplied in the hatSigma-argument.

Usage

pffrGLS(
  formula,
  yind,
  hatSigma,
  algorithm = NA,
  method = "REML",
  tensortype = c("te", "t2"),
  bs.yindex = list(bs = "ps", k = 5, m = c(2, 1)),
  bs.int = list(bs = "ps", k = 20, m = c(2, 1)),
  cond.cutoff = 500,
  ...
)

Arguments

`formula`	a formula with special terms as for `gam`, with additional special terms `ff()` and `c()`. See `pffr`.
`yind`	a vector with length equal to the number of columns of the matrix of functional responses giving the vector of evaluation points `(t_1, \dots ,t_{G})`. see `pffr`
`hatSigma`	(an estimate of) the within-observation covariance (along the responses' index), evaluated at `yind`. See Details.
`algorithm`	the name of the function used to estimate the model. Defaults to `gam` if the matrix of functional responses has less than `2e5` data points and to `bam` if not. "gamm" (see `gamm`) and "gamm4" (see `gamm4`) are valid options as well.
`method`	See `pffr`
`tensortype`	See `pffr`
`bs.yindex`	See `pffr`
`bs.int`	See `pffr`
`cond.cutoff`	if the condition number of `hatSigma` is greater than this, `hatSigma` is made “more” positive-definite via `nearPD` to ensure a condition number equal to cond.cutoff. Defaults to 500.
`...`	additional arguments that are valid for `gam` or `bam`. See `pffr`.

Value

a fitted pffr-object, see pffr.

Details

Note that hatSigma has to be positive definite. If hatSigma is close to positive semi-definite or badly conditioned, estimated standard errors become unstable (typically much too small). pffrGLS will try to diagnose this and issue a warning. The danger is especially big if the number of functional observations is smaller than the number of gridpoints (i.e, length(yind)), since the raw covariance estimate will not have full rank.
Please see pffr for details on model specification and implementation.
THIS IS AN EXPERIMENTAL VERSION AND NOT WELL TESTED YET – USE AT YOUR OWN RISK.

Author(s)

Fabian Scheipl