Support for K matrix with loading matrix Z #292
Description
Hi, first of all sorry to not post this in google group, similar to #291 I can't seem to access the content.
In the current version of gemma, the K matrix must be positive definite with nxn dimension, where n is the number of samples. However, in the original Zhou & Stephens publication, for cases with multiple samples from the same genetic strain, it is allowed to specify an mxm K matrix where m is the number of unique strains, and then use a nxm loading matrix Z to map each sample to a strain. As far as I understand, the ZK combination is not an option, and if I pre-expand K by doing K' = ZKZ^T, it will make the K' matrix non-positive definite and get gemma to throw an error.
Would it be possible to relax the positive definiteness restriction on K? Alternatively, what are the theoretical or computational downsides of allowing such a K matrix? Thanks in advance for your time and consideration!
