Returns estimated coefficient functions/surfaces \(\beta(t), \beta(s,t)\) and estimated smooth effects \(f(z), f(x,z)\) or \(f(x, z, t)\) and their point-wise estimated standard errors. Not implemented for smooths in more than 3 dimensions.
# S3 method for pffr coef( object, raw = FALSE, se = TRUE, freq = FALSE, sandwich = FALSE, seWithMean = TRUE, n1 = 100, n2 = 40, n3 = 20, Ktt = NULL, ... )
logical, defaults to FALSE. If TRUE, the function simply returns
logical, defaults to TRUE. Return estimated standard error of the estimates?
logical, defaults to FALSE. If FALSE, use posterior variance
object$Vp for variability estimates,
logical, defaults to FALSE. Use a Sandwich-estimator for approximate variances? See Details. THIS IS AN EXPERIMENTAL FEATURE, USE A YOUR OWN RISK.
logical, defaults to TRUE. Include uncertainty about the intercept/overall mean in standard errors returned for smooth components?
n1, n2, n3 give the number of gridpoints for 1-/2-/3-dimensional smooth terms
used in the marginal equidistant grids over the range of the covariates at which the estimated effects are evaluated.
(optional) an estimate of the covariance operator of the residual process \(\epsilon_i(t) \sim N(0, K(t,t'))\),
object. If not supplied, this is estimated from the crossproduct matrices of the
observed residual vectors. Only relevant for sandwich CIs.
other arguments, not used.
raw==FALSE, a list containing
pterms a matrix containing the parametric / non-functional coefficients (and, optionally, their se's)
smterms a named list with one entry for each smooth term in the model. Each entry contains
coef a matrix giving the grid values over the covariates, the estimated effect (and, optionally, the se's).
The first covariate varies the fastest.
x, y, z the unique gridpoints used to evaluate the smooth/coefficient function/coefficient surface
xlim, ylim, zlim the extent of the x/y/z-axes
xlab, ylab, zlab the names of the covariates for the x/y/z-axes
dim the dimensionality of the effect
main the label of the smooth term (a short label, same as the one used in
seWithMean-option corresponds to the
sandwich-options works as follows: Assuming that the residual vectors \(\epsilon_i(t), i=1,\dots,n\) are i.i.d.
realizations of a mean zero Gaussian process with covariance \(K(t,t')\), we can construct an estimator for
\(K(t,t')\) from the \(n\) replicates of the observed residual vectors. The covariance matrix of the stacked observations
vec\((Y_i(t))\) is then given by a block-diagonal matrix with \(n\) copies of the estimated \(K(t,t')\) on the diagonal.
This block-diagonal matrix is used to construct the "meat" of a sandwich covariance estimator, similar to Chen et al. (2012),
see reference below.
Chen, H., Wang, Y., Paik, M.C., and Choi, A. (2013). A marginal approach to reduced-rank penalized spline smoothing with application to multilevel functional data. Journal of the American Statistical Association, 101, 1216--1229.