Subhadeep Mukhopadhyay writes:

I am convinced of the power of hierarchical modeling and individual parameter pooling concept. I was wondering how could multi-level modeling could influence the estimate of grad mean (NOT individual label).

My reply: Multilevel modeling will affect the estimate of the grand mean in two ways:

1. If the group-level mean is correlated with group size, then the partial pooling will change the estimate of the grand mean (and, indeed, you might want to include group size or some similar variable as a group-level predictor.

2. In any case, the extra error term(s) in a multilevel model will typically affect the standard error of everything, including the estimate of the grand mean.