lf_old: Construct an FLM regression term

In refund: Regression with Functional Data

Construct an FLM regression term

Description

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

Usage

lf_old(
  X,
  argvals = seq(0, 1, l = ncol(X)),
  xind = NULL,
  integration = c("simpson", "trapezoidal", "riemann"),
  L = NULL,
  splinepars = list(bs = "ps", k = min(ceiling(n/4), 40), m = c(2, 2)),
  presmooth = TRUE
)

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 not be supported in the next version of refund.
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	an optional N by ncol(argvals) matrix giving the weights for the numerical integration over t
splinepars	optional arguments specifying options for representing and penalizing the functional coefficient \beta(t). Defaults to a cubic B-spline with second-order difference penalties, i.e. list(bs="ps", m=c(2, 1)) See te or s for details
presmooth	logical; if true, the functional predictor is pre-smoothed prior to fitting. See smooth.basisPar

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 lf

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

7. presmooth - the presmooth argument supplied to lf

8. 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

See Also

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

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