refund (version 0.1-23)

sff: Construct a smooth function-on-function regression term


Defines a term \(\int^{s_{hi, i}}_{s_{lo, i}} f(X_i(s), s, t) ds\) for inclusion in an mgcv::gam-formula (or bam or gamm or gamm4:::gamm) as constructed by pffr. Defaults to a cubic tensor product B-spline with marginal second differences penalties for \(f(X_i(s), s, t)\) and integration over the entire range \([s_{lo, i}, s_{hi, i}] = [\min(s_i), \max(s_i)]\). Can't deal with any missing \(X(s)\), unequal lengths of \(X_i(s)\) not (yet?) possible. Unequal ranges for different \(X_i(s)\) should work. \(X_i(s)\) is assumed to be numeric. sff() IS AN EXPERIMENTAL FEATURE AND NOT WELL TESTED YET -- USE AT YOUR OWN RISK.


  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))



an n by ncol(xind) matrix of function evaluations \(X_i(s_{i1}),\dots, X_i(s_{iS})\); \(i=1,\dots,n\).


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


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


defaults to "te", i.e. a tensor product spline to represent \(f(X_i(s), t)\). 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. Alternatively and for non-equidistant grids, "trapezoidal".


optional: an n by ncol(xind) giving the weights for the numerical integration over \(s\).


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


optional arguments supplied to the basistype-term. Defaults to a cubic tensor product B-spline with marginal second differences, i.e. list(bs="ps", m=c(2,2,2)). See te or s for details


a list containing

  • call a "call" to te (or s, t2) using the appropriately constructed covariate and weight matrices (see linear.functional.terms)

  • data a list containing the necessary covariate and weight matrices