Usage
af(X, xind = seq(0, 1, l = ncol(X)), 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)Arguments
X
an N by J=ncol(xind) matrix of function evaluations $X_i(t_{i1}),., X_i(t_{iJ}); i=1,.,N.$
xind
matrix (or vector) of indices of evaluations of $X_i(t)$; i.e. a matrix with ith row $(t_{i1},.,t_{iJ})$.
basistype
defaults to "te", i.e. a tensor product spline to represent $F(x,t)$ Alternatively, use "s" for bivariate basis functions (see mgcv's s) or "t2" for an alternative parameter 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" integrati
L
optional: an N by ncol(xind) matrix giving the weights for the numerical integration over t.
splinepars
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 <
presmooth
If true, the functional predictor is pre-smoothed prior to fitting. See smooth.basisPar in package fda Xrange
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 rang
Qtransform
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