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patperry / r-mbest

Moment-Based Estimation for Hierarchical Models (R Package)
Apache License 2.0
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What is the subspace in the final output of mhglm() #4

Open pingqingsheng opened 7 years ago

pingqingsheng commented 7 years ago

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 commented 7 years ago

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.