R: Utility functions for constructing tensor product smooths

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

## Utility functions for constructing tensor product smooths

### 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.

### Usage

    tensor.prod.model.matrix(X)
    tensor.prod.penalties(S)

### 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.

### 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!

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

    X <- list(matrix(1:4,2,2),matrix(5:10,2,3))
    tensor.prod.model.matrix(X)

    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 1.4-1.1 Index]