af_old: Construct an FGAM regression term

In refund: Regression with Functional Data

Construct an FGAM regression term

Description

Defines a term \int_{T}F(X_i(t),t)dt for inclusion in an mgcv::gam-formula (or {bam} or {gamm} or gamm4:::gamm) as constructed by {fgam}, where F(x,t)$ is an unknown smooth bivariate function and X_i(t) is a functional predictor on the closed interval T. Defaults to a cubic tensor product B-spline with marginal second-order difference penalties for estimating F(x,t). The functional predictor must be fully observed on a regular grid

Usage

af_old(
  X,
  argvals = seq(0, 1, l = ncol(X)),
  xind = NULL,
  basistype = c("te", "t2", "s"),
  integration = c("simpson", "trapezoidal", "riemann"),
  L = NULL,
  splinepars = list(bs = "ps", k = c(min(ceiling(nrow(X)/5), 20), min(ceiling(ncol(X)/5),
    20)), m = list(c(2, 2), c(2, 2))),
  presmooth = TRUE,
  Xrange = range(X),
  Qtransform = FALSE
)

Arguments

X	an N by J=ncol(argvals) matrix of function evaluations X_i(t_{i1}),., X_i(t_{iJ}); i=1,.,N.
argvals	matrix (or vector) of indices of evaluations of X_i(t); i.e. a matrix with ith row (t_{i1},.,t_{iJ})
xind	Same as argvals. It will discard this argument in the next version of refund.
basistype	defaults to "te", i.e. a tensor product spline to represent F(x,t) Alternatively, use "s" for bivariate basis functions (see {s}) or "t2" for an alternative parameterization of tensor product splines (see {t2})
integration	method used for numerical integration. Defaults to "simpson"'s rule for calculating entries in L. Alternatively and for non-equidistant grids, "trapezoidal" or "riemann". "riemann" integration is always used if L is specified
L	optional weight matrix for the linear functional
splinepars	optional arguments specifying options for representing and penalizing the function F(x,t). Defaults to a cubic tensor product B-spline with marginal second-order difference penalties, i.e. list(bs="ps", m=list(c(2, 2), c(2, 2)), see {te} or {s} for details
presmooth	logical; if true, the functional predictor is pre-smoothed prior to fitting; see {smooth.basisPar}
Xrange	numeric; range to use when specifying the marginal basis for the x-axis. It may be desired to increase this slightly over the default of range(X) if concerned about predicting for future observed curves that take values outside of range(X)
Qtransform	logical; should the functional be transformed using the empirical cdf and applying a quantile transformation on each column of X prior to fitting? This ensures Xrange=c(0,1). If Qtransform=TRUE and presmooth=TRUE, presmoothing is done prior to transforming the functional predictor

Value

A list with the following entries:

1. call - a "call" to te (or s, t2) using the appropriately constructed covariate and weight matrices.

2. argvals - the argvals argument supplied to af

3. L-the matrix of weights used for the integration

4. xindname - the name used for the functional predictor variable in the formula used by mgcv.

5. tindname - the name used for argvals variable in the formula used by mgcv

6. Lname - the name used for the L variable in the formula used by mgcv

7. presmooth - the presmooth argument supplied to af

8. Qtranform - the Qtransform argument supplied to af

9. Xrange - the Xrange argument supplied to af

10. ecdflist - a list containing one empirical cdf function from applying {ecdf} to each (possibly presmoothed) column of X. Only present if Qtransform=TRUE

11. Xfd - an fd object from presmoothing the functional predictors using {smooth.basisPar}. Only present if presmooth=TRUE. See {fd}.

Author(s)

Mathew W. McLean [e-mail] and Fabian Scheipl

References

McLean, M. W., Hooker, G., Staicu, A.-M., Scheipl, F., and Ruppert, D. (2014). Functional generalized additive models. Journal of Computational and Graphical Statistics, 23 (1), pp. 249-269.

See Also

{fgam}, {lf}, mgcv's {linear.functional.terms}, {fgam} for examples

refund documentation built on Sept. 21, 2024, 1:07 a.m.