pcre: pffr-constructor for PC-basis functional random effects
Description
Fits functional random effects, by restricting them to the span of the leading eigenfunctions of the functional covarianceUsage
pcre(id, efunctions, evalues, yind)
Arguments
id
grouping variable: a factor.
efunctions
matrix of eigenfunction evaluations on
grid points yind (yind> x ).
evalues
eigenvalues associated with
efunctions.
yind
vector of grid points on which responses
$Y(t)$ are evaluated.
Value
- a list used internally for constructing an appropriate
call to
mgcv::gam
Details
pcre
fits functional random effects $B_i(t)$ for a
grouping variable id, using as a basis the
eigenfunctions $\phi_m(t)$ in efunctions with
eigenvalues $\lambda_m$ in evalues:
$B_i(t) \approx \sum_m^M \phi_m(t)\delta_{im}$ with
independent $\delta_{im} \sim N(0,
\sigma^2\lambda_m)$, where $\sigma^2$ is estimated
and controls the overall contribution of the $B_i(t)$,
while the relative importance of the $M$
eigenfunctions is controlled by the supplied eigenvalues
evalues. Can be used to model smooth residual functions if
id is simply an index of functional observations. This is an
experimental feature and not well tested yet, use at your
own risk.