coef.pffr: Get estimated coefficients from a pffr fit

Description

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.

Usage

# S3 method for pffr
coef(
  object,
  raw = FALSE,
  se = TRUE,
  freq = FALSE,
  sandwich = FALSE,
  seWithMean = TRUE,
  n1 = 100,
  n2 = 40,
  n3 = 20,
  Ktt = NULL,
  ...
)

Value

If 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 summary.pffr)

Arguments

object: a fitted pffr-object
raw: logical, defaults to FALSE. If TRUE, the function simply returns object$coefficients
se: logical, defaults to TRUE. Return estimated standard error of the estimates?
freq: logical, defaults to FALSE. If FALSE, use posterior variance object$Vp for variability estimates, else use object$Ve. See gamObject
sandwich: logical, defaults to FALSE. Use a Sandwich-estimator for approximate variances? See Details. THIS IS AN EXPERIMENTAL FEATURE, USE A YOUR OWN RISK.
seWithMean: logical, defaults to TRUE. Include uncertainty about the intercept/overall mean in standard errors returned for smooth components?
n1: see below
n2: see below
n3: 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.
Ktt: (optional) an estimate of the covariance operator of the residual process $\epsilon_i(t) \sim N(0, K(t,t'))$, evaluated on yind of 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.

Author

Fabian Scheipl

Details

The seWithMean-option corresponds to the "iterms"-option in predict.gam. 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.

References

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.