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.