Combining LOO-CV across equivalent models over independent datasets

[avehtari]

@sammosummo

I feel like this approach is equivalent to fitting a single candidate model to all data but without partial pooling . With so much data per submodel, I know partial pooling doesn’t make much of a difference to the submodel parameter estimates. Besides losing partial pooling, is there anything else disadvantageous about this approach?

No.

@sammosummo

If I have the estimates LOOIC, number of effective parameters, and se of LOOIC per submodel, how to I combine them to get an estimate of the supermodel’s LOOIC?

For combing elpd, elpd_se, elpd_diff, and elpd_diff_se from separate models, see
Adding elpd_kfold estimates from several models to create composite elpd_kfold for comparison - #2 by avehtari and the rest of the thread. I’ll add this to my CV-FAQ soon. For how elpd and LOOIC are related and why I prefer elpd see 21 in CV-FAQ.