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
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
)
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}
.
an N
by J=ncol(argvals)
matrix of function evaluations
\(X_i(t_{i1}),., X_i(t_{iJ}); i=1,.,N.\)
matrix (or vector) of indices of evaluations of \(X_i(t)\); i.e. a matrix with ith row \((t_{i1},.,t_{iJ})\)
Same as argvals. It will discard this argument in the next version of refund.
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}
)
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
optional weight matrix for the linear functional
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
logical; if true, the functional predictor is pre-smoothed prior to fitting; see
{smooth.basisPar}
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)
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
Mathew W. McLean mathew.w.mclean@gmail.com and Fabian Scheipl
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.
{fgam}
, {lf}
, mgcv's {linear.functional.terms}
,
{fgam}
for examples