Description Usage Arguments Details Value Author(s) References See Also
Defines a term \int^{s_{hi, i}}_{s_{lo, i}} X_i(s)β(t,s)ds for
inclusion in an mgcv::gam
formula (or bam
or gamm
or
gamm4:::gamm4
) as constructed by pffr
.
Defaults to a
cubic tensor product Bspline with marginal first order differences penalties
for β(t,s) and numerical integration over the entire range
[s_{lo, i}, s_{hi, i}] = [\min(s_i), \max(s_i)] by using Simpson
weights. Can't deal with any missing X(s), unequal lengths of
X_i(s) not (yet?) possible. Unequal integration ranges for different
X_i(s) should work. X_i(s) is assumed to be numeric (duh...).
1 2 3 4 5 6 7 8 9 10 11 12  ff(
X,
yind = NULL,
xind = seq(0, 1, l = ncol(X)),
basistype = c("te", "t2", "ti", "s", "tes"),
integration = c("simpson", "trapezoidal", "riemann"),
L = NULL,
limits = NULL,
splinepars = if (basistype != "s") { list(bs = "ps", m = list(c(2, 1), c(2, 1)),
k = c(5, 5)) } else { list(bs = "tp", m = NA) },
check.ident = TRUE
)

X 
an n by 
yind 
DEPRECATED used to supply matrix (or vector) of indices of evaluations of Y_i(t), no longer used. 
xind 
vector of indices of evaluations of X_i(s), i.e, (s_{1},…,s_{S}) 
basistype 
defaults to " 
integration 
method used for numerical integration. Defaults to

L 
optional: an n by 
limits 
defaults to NULL for integration across the entire range of
X(s), otherwise specifies the integration limits s_{hi}(t),
s_{lo}(t): either one of 
splinepars 
optional arguments supplied to the 
check.ident 
check identifiability of the model spec. See Details and
References. Defaults to 
If check.ident==TRUE
and basistype!="s"
(the default), the
routine checks conditions for nonidentifiability of the effect. This occurs
if a) the marginal basis for the functional covariate is rankdeficient
(typically because the functional covariate has lower rank than the spline
basis along its index) and simultaneously b) the kernel of Cov(X(s)) is
not disjunct from the kernel of the marginal penalty over s
. In
practice, a) occurs quite frequently, and b) occurs usually because
curvewise mean centering has removed all constant components from the
functional covariate.
If there is kernel overlap, β(t,s) is
constrained to be orthogonal to functions in that overlap space (e.g., if the
overlap contains constant functions, constraints "\int β(t,s) ds =
0 for all t" are enforced). See reference for details.
A warning is
always given if the effective rank of Cov(X(s)) (defined as the number
of eigenvalues accounting for at least 0.995 of the total variance in
X_i(s)) is lower than 4. If X_i(s) is of very low rank,
ffpc
term may be preferable.
A list containing
call 
a "call" to

data 
a list containing the necessary covariate and weight matrices 
Fabian Scheipl, Sonja Greven
For background on check.ident
:
Scheipl, F., Greven,
S. (2016). Identifiability in penalized functiononfunction regression
models. Electronic Journal of Statistics, 10(1), 495–526.
https://projecteuclid.org/journals/electronicjournalofstatistics/volume10/issue1/Identifiabilityinpenalizedfunctiononfunctionregressionmodels/10.1214/16EJS1123.full
mgcv
's linear.functional.terms
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