sff.Rd

% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/pffr-sff.R
\name{sff}
\alias{sff}
\title{Construct a smooth function-on-function regression term}
\usage{
sff(
  X,
  yind,
  xind = seq(0, 1, l = ncol(X)),
  basistype = c("te", "t2", "s"),
  integration = c("simpson", "trapezoidal"),
  L = NULL,
  limits = NULL,
  splinepars = list(bs = "ps", m = c(2, 2, 2))
)
}
\arguments{
\item{X}{an n by \code{ncol(xind)} matrix of function evaluations
\eqn{X_i(s_{i1}),\dots, X_i(s_{iS})}; \eqn{i=1,\dots,n}.}

\item{yind}{\emph{DEPRECATED} matrix (or vector) of indices of evaluations of
\eqn{Y_i(t)}; i.e. matrix with rows \eqn{(t_{i1},\dots,t_{iT})}; no longer
used.}

\item{xind}{vector of indices of evaluations of \eqn{X_i(s)},
i.e, \eqn{(s_{1},\dots,s_{S})}}

\item{basistype}{defaults to "\code{\link[mgcv]{te}}", i.e. a tensor product
spline to represent \eqn{f(X_i(s), t)}. Alternatively, use \code{"s"} for
bivariate basis functions (see \code{\link[mgcv]{s}}) or \code{"t2"} for an
alternative parameterization of tensor product splines (see
\code{\link[mgcv]{t2}}).}

\item{integration}{method used for numerical integration. Defaults to
\code{"simpson"}'s rule. Alternatively and for non-equidistant grids,
\code{"trapezoidal"}.}

\item{L}{optional: an n by \code{ncol(xind)} giving the weights for the
numerical integration over \eqn{s}.}

\item{limits}{defaults to NULL for integration across the entire range of
\eqn{X(s)}, otherwise specifies the integration limits \eqn{s_{hi, i},
s_{lo, i}}: either one of \code{"s<t"} or \code{"s<=t"} for \eqn{(s_{hi,
i}, s_{lo, i}) = (0, t)} or a function that takes \code{s} as the first and
\code{t} as the second argument and returns TRUE for combinations of values
\code{(s,t)} if \code{s} falls into the integration range for the given
\code{t}. This is an experimental feature and not well tested yet; use at
your own risk.}

\item{splinepars}{optional arguments supplied to the \code{basistype}-term.
Defaults to a cubic tensor product B-spline with marginal second
differences, i.e. \code{list(bs="ps", m=c(2,2,2))}. See
\code{\link[mgcv]{te}} or \code{\link[mgcv]{s}} for details}
}
\value{
a list containing \itemize{ \item \code{call} a "call" to
  \code{\link[mgcv]{te}} (or \code{\link[mgcv]{s}}, \code{\link[mgcv]{t2}})
  using the appropriately constructed covariate and weight matrices (see
  \code{\link[mgcv]{linear.functional.terms}}) \item \code{data} a list
  containing the necessary covariate and weight matrices }
}
\description{
Defines a term \eqn{\int^{s_{hi, i}}_{s_{lo, i}} f(X_i(s), s, t) ds} for
inclusion in an \code{mgcv::gam}-formula (or \code{bam} or \code{gamm} or
\code{gamm4:::gamm}) as constructed by \code{\link{pffr}}. Defaults to a
cubic tensor product B-spline with marginal second differences penalties for
\eqn{f(X_i(s), s, t)} and integration over the entire range \eqn{[s_{lo, i},
s_{hi, i}] = [\min(s_i), \max(s_i)]}. Can't deal with any missing \eqn{X(s)},
unequal lengths of \eqn{X_i(s)} not (yet?) possible. Unequal ranges for
different \eqn{X_i(s)} should work. \eqn{X_i(s)} is assumed to be numeric.\cr
\code{sff()} IS AN EXPERIMENTAL FEATURE AND NOT WELL TESTED YET -- USE AT
YOUR OWN RISK.
}
\author{
Fabian Scheipl, based on Sonja Greven's trick for fitting functional
  responses.
}