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.

```
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
)
```

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
*i*th 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

presmooth

logical; if true, the functional predictor is pre-smoothed prior to fitting. See
`smooth.basisPar`

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`lf`

`L`

- the matrix of weights used for the integrationxindname - 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`

`LXname`

- the name used for the`L`

variable in the`formula`

used by`mgcv`

`presmooth`

- the`presmooth`

argument supplied to`lf`

`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