# coef.pffr: Get estimated coefficients from a pffr fit In refund: Regression with Functional Data

## Description

Returns estimated coefficient functions/surfaces β(t), β(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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```## S3 method for class 'pffr' coef( object, raw = FALSE, se = TRUE, freq = FALSE, sandwich = FALSE, seWithMean = TRUE, n1 = 100, n2 = 40, n3 = 20, Ktt = NULL, ... ) ```

## 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 ε_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.

## Details

The `seWithMean`-option corresponds to the `"iterms"`-option in `predict.gam`. The `sandwich`-options works as follows: Assuming that the residual vectors ε_i(t), i=1,…,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.

## 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`)

Fabian Scheipl

## 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.

`plot.gam`, `predict.gam` which this routine is based on.