refund: af_old – R documentation

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af_old

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:

call - a "call" to te (or s, t2) using the appropriately constructed covariate and weight matrices.
argvals - the argvals argument supplied to af
L the matrix of weights used for the integration

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

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

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

presmooth - the presmooth argument supplied to af

Qtranform - the Qtransform argument supplied to af

Xrange - the Xrange argument supplied to af

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

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

Author(s)

Mathew W. McLean mathew.w.mclean@gmail.com 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. Available at https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3982924/.