What is the subspace in the final output of mhglm()

[pingqingsheng]

Hi, I'm trying to use this package in my course project, but I can't find corresponding value of "subspace" in the final output to its counterpart in the paper. What is the subspace in the final output of mhglm() ? I thought it was the right singular matrix (full column rank part) of the data matrix, that is V_i, but it isn't.

Could someone gives me brief explanation ?

Thanks

[patperry]

The subspace and precision give you the eigendecomposition of the group-specific precision matrix (corresponding to V_i and D_i^{-2} in the paper). These are computed using the precision matrix returned from firthglm.fit.

The description of V_i and D_i in section 3.4 of the paper is slightly different than in the R package. Up to numerical error, you will get the same weights with either choice, but in the paper's version, D_i is not diagonal.