vows (version 0.5)

qplsc.mp: Quadratically penalized least squares with constraints

Description

Fits a possibly very large number of models, with common design matrix, by quadratically penalized least squares, with identifiability constraints imposed. This function serves as the fitting engine for semipar.mp.

Usage

qplsc.mp(Y, modmat, penmat, constr.list = NULL, lsp, nulldim = NULL, store.reml = FALSE, store.fitted = FALSE)

Arguments

Y

an $n \times V$ response matrix ($V$ refers to number of models fitted in parallel, e.g., voxels in neuroimaging applications).

modmat

model matrix, e.g., a matrix of B-spline basis functions.

penmat

penalty matrix.

constr.list

a list of length equal to number of constraints to be imposed, containing information for reparametization to an unconstrained optimization. Attribute 'C' is the constraint matrix, and 'start' and 'end' refer to the corresponding column positions of the model matrix.

lsp

vector of candidate tuning parameters ($\log(\lambda)$).

nulldim

null space dimension, ordinarily equal to the order of the derivative penalty.

store.reml

logical: should the pointwise REML criterion at each grid point be included in the output? FALSE by default, as this output can be very large.

store.fitted

logical: should the fitted values be included in the output? FALSE by default.

Value

An object of class "qplsc.mp", which is a list with elements: , which is a list with elements:

References

Reiss, P. T., Huang, L., Chen, Y.-H., Huo, L., Tarpey, T., and Mennes, M. (2014). Massively parallel nonparametric regression, with an application to developmental brain mapping. Journal of Computational and Graphical Statistics, Journal of Computational and Graphical Statistics, 23(1), 232--248.

Wood, S. N. (2004). Stable and efficient multiple smoothing parameter estimation for generalized additive models. Journal of the American Statistical Association, 99, 673--686.

Examples

## see semipar.mp