tensor.prod.model.matrix {mgcv}R Documentation

Row Kronecker product/ tensor product smooth construction

Description

Produce model matrices or penalty matrices for a tensor product smooth from the model matrices or penalty matrices for the marginal bases of the smooth. The model matrix construction uses row Kronecker products.

Usage

tensor.prod.model.matrix(X)
tensor.prod.penalties(S)
a%.%b

Arguments

X

a list of model matrices for the marginal bases of a smooth

S

a list of penalties for the marginal bases of a smooth.

a

a matrix with the same number of rows as A.

b

a matrix with the same number of rows as B.

Details

If X[[1]], X[[2]] ... X[[m]] are the model matrices of the marginal bases of a tensor product smooth then the ith row of the model matrix for the whole tensor product smooth is given by X[[1]][i,]%x%X[[2]][i,]%x% ... X[[m]][i,], where %x% is the Kronecker product. Of course the routine operates column-wise, not row-wise!

A%.%B is the operator form of this ‘row Kronecker product’.

If S[[1]], S[[2]] ... S[[m]] are the penalty matrices for the marginal bases, and I[[1]], I[[2]] ... I[[m]] are corresponding identity matrices, each of the same dimension as its corresponding penalty, then the tensor product smooth has m associate penalties of the form:

S[[1]]%x%I[[2]]%x% ... I[[m]],

I[[1]]%x%S[[2]]%x% ... I[[m]]

...

I[[1]]%x%I[[2]]%x% ... S[[m]].

Of course it's important that the model matrices and penalty matrices are presented in the same order when constructing tensor product smooths.

Value

Either a single model matrix for a tensor product smooth, or a list of penalty terms for a tensor product smooth.

Author(s)

Simon N. Wood simon.wood@r-project.org

References

Wood, S.N. (2006) Low rank scale invariant tensor product smooths for Generalized Additive Mixed Models. Biometrics 62(4):1025-1036

See Also

te, smooth.construct.tensor.smooth.spec

Examples

require(mgcv)
X <- list(matrix(1:4,2,2),matrix(5:10,2,3))
tensor.prod.model.matrix(X)
X[[1]]%.%X[[2]]

S<-list(matrix(c(2,1,1,2),2,2),matrix(c(2,1,0,1,2,1,0,1,2),3,3))
tensor.prod.penalties(S)


[Package mgcv version 1.8-31 Index]