plsfitCV: Penalized Least Square Fit under CV
In funstatpackages/GgAM: Generalized geoAdditive Models

Description Usage Arguments Details Value Examples

This is an internal function of package ggam.

1	plsfitCV(B, Q2, K, lambda, Y, fx, fold = 5, Z = NULL)

`B`	The bernstein basis matrix.
`Q2`	The `Q2` matrix from QR decomposition of the transpose of the constraint matrix.
`K`	The energy matrix to construct penalty matrix.
`lambda`	The smoothing penalty parameter.
`Y`	Response variable.
`fx`	indicates whether the term is a fixed d.f. regression. spline (`TRUE`) or a penalized regression spline (`FALSE`).
`fold`	number of folders to do cross validation.
`Z`	The parametric model matrix. set to '`NULL`' if it is not provided.

The method is a computationally efficient means of applying cross validation to the problem of smoothing parameter selection:

\min _ { \boldsymbol { β } , \boldsymbol { γ } } \frac { 1 } { 2 } ≤ft{ \| \mathbf { Y } - \mathbf { Z } \boldsymbol { β } - \mathbf { B } \boldsymbol { γ } \| ^ { 2 } + λ \boldsymbol { γ } ^ { \top } \mathbf { P } γ \right}

subject to constraints \mathbf { H } γ = \mathbf { 0 }. Z is a parametrix design matrix, β a parameter vector, Y a data vector, γ is the berstein coefficients, B is the Bernsterin basis matrix, H is contraint matrix.

A list of fit information.

library(GgAM)
library(Matrix)
library(BPST)
data("eg2pop_dat")
eg2_V20=eg2pop_dat[['V20']]
eg2_T20=eg2pop_dat[['T20']]
eg2pop=eg2pop_dat[['pop']]
d=2
r=1
sam=eg2pop[sample(1:dim(eg2pop)[1],100),]
B0=basis(eg2_V20,eg2_T20, d, r, sam[,3:4])
B=B0$Bi
ind=B0$Ind.inside
Q2=B0$Q2
K=B0$K
Z=sam[ind,c(5:12)]
Y=sam[ind,'Y']
lambda=10^(seq(-2,5,by=1))
plsfitCV(as.matrix(B),Q2,K,lambda,Y,fx=FALSE,Z=Z)
### without parametric part
plsfitCV(as.matrix(B),Q2,K,lambda,Y,fx=FALSE)