Still, it is a) quite likely there is a problem with the model, so running with a subset and simpler model first is definitely a good step (because it let’s you iterate much faster). Issues with the model also frequently mean the model samples much slower (a.k.a. the “folk theorem”) and b) you might want to consider using an approximation: INLA is quite a good package for approximate multilevel models if your model can fit this box. But point a) still holds even there - especially testing the smaller model/data works with Stan, checking the results on smaller model data are the same between Stan and INLA and then running INLA for the big model is IMHO a very robust workflow.
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