refund (version 0.1-23)

# lf_old: Construct an FLM regression term

## Description

Defines a term $$\int_{T}\beta(t)X_i(t)dt$$ for inclusion in an gam-formula (or bam or gamm or 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

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