No pooling vs independent fit

Modeling
1

Dear all,

Consider the scenario where there are N subjects each with at least n data points.
I am trying to figure out the difference between fitting a multilevel regression model assuming No Pool to all subjects and fitting the regression model separately to each subject.

  1. Do the two modelling approaches imply that each subject is independent (that is has its own parameters)?

I have asked for a clarification of the two approaches as I am told to fit a model separately to each subject data, but then I am wondering if wouldn’t this be same as fitting a multilevel No Pool model.

Thanks for the help

2

I moved to the modeling category and can answer.

No, those two things are not the same if there are shared parameters. For a simple logistic regression with only an intercept, they’d be the same. For a linear regression you’d have to decide what to do with the error scale parameter.

We almost always recommend fitting the hierarchical model with a weakly informative prior on the hyperparameters. That way, the data determines how much pooling is appropriate.