[ADMB Users] asreml ar(1) x ar(1) spatial model

[dave fournier]

> As a user who is struggling with spatial issues, I'd love to see this part of the ADMB website fleshed out more - potentially as a first step towards such a workshop. Kasper's example that is there at the moment is pretty dense and hard to make headway with for to those of us that are not familar with the finer points of spatial modelling...  Part of the problem I found is the sparse-matrix aspect of the example - maybe it could be good to have a simpler instructive example where it is done by "brute-force" first (e.g. on a 10x 10 matrix, so that it is feasible), and then have the sparse-matrix extension once people understand that.
>
> Another suggestion for a more general approach could be to build up a section on "incoporating correlation structures"? i.e. simple examples of how to do AR(1) processes, temporal and spatial correlations... The book by Zuur et al 2009 "Mixed Effects Models and Extensions in Ecology with R" has some nice examples in this direction that could easily be solved in ADMB as worked examples...
>
> Mark

Did you look at my reworking of Kaspar's code.  I think it clears up the 
main
conceptual difficulty  which is that he addresses an essentially 2 
dimensional
object (the random effects) as a one dimensional one. Once you do that
you can see that the prior is a special case of

          sum_i,j,k,l   u_ij *u_kl *a_ik *b_jl

and all you need to do is to keep track of which of these terms are non 
zero.
It turns out that the a_ik and b_jl are both tridiagonal matrices with 
only 3 different
entries so you just need to identify the entry type.