mgcv's gam and its siblings to
fit models of the general form
$Y_i(t) = \mu(t) +
\int X_i(s)\beta(s,t)ds + f(z_{1i}, t) + f(z_{2i}) +
z_{3i} \beta_3(t) + \dots + E_i(t))$
with a functional
(but not necessarily continuous) response $Y(t)$,
(optional) smooth intercept $\mu(t)$, (multiple)
functional covariates $X(t)$ and scalar covariates
$z_1$, $z_2$, etc. The residual functions
$E_i(t) \sim GP(0, K(t,t'))$ are assumed to be i.i.d.
realizations of a Gaussian process. An estimate of the
covariance operator $K(t,t')$ evaluated on
yind has to be supplied in the
hatSigma-argument. Note that this has to be
positive definite. If hatSigma is close to
positive semi-definite or badly conditioned,
estimated standard errors become unstable (typically much
too small). pffrGLS will try to diagnose this and
issue a warning. The danger is especially big if the
number of functional observations is smaller than the
number of gridpoints (i.e, length(yind)), since
the raw covariance estimate will not have full rank.pffrGLS(formula, yind, hatSigma, algorithm = NA,
method = "REML", tensortype = c("te", "t2"),
bs.yindex = list(bs = "ps", k = 5, m = c(2, 1)),
bs.int = list(bs = "ps", k = 20, m = c(2, 1)),
cond.cutoff = 500, ...)pffryind. See Details.pffrpffrpffrpffrhatSigma is greater than this, hatSigma is
made ``more'' positive-definite via
nearPD to ensure a condition number
equal to cond.cutoff. Defpffr-object, see
pffr.pffr for details on
model specification and implementation.
THIS IS AN
EXPERIMENTAL VERSION AND NOT WELL TESTED YET -- USE AT
YOUR OWN RISK.pffr, fpca.sc