# Am I doing hierarchical bayesian regression?

I'm doing a Bayesian logistic regression to predict the probability of my dependent variable Y with two predictors, one continuous (X) and the other categorical (C). I deal with C by building 3 models of Y ~ X where 3 is the number of levels of C (levels=a,b,c).

Now, I also have a second categorical variable C2 which is a sub-category of C. C2 has sub-categories a1,a2 (parent=level a of C), b1,b2,b3 (parent=level b of C) and c1,c2 (parent=level c of C). To deal with C2, I'm doing 7 logistic regressions where I use as my priors the ones I derived from the 3 models above.

For example, if model 1 (which models Y ~ X for level a of C) shows gaussian traces with mean m and standard deviation s, I use m and s for the normal priors of the two sub-models (which model Y ~ X for sublevels a1 and a2 respectively).

Questions: does it make sense to proceed like that? if yes, is it what is called hierarchical bayesian regression?

• Thanks @Tim, very appreciated. What is not clear for me is the following: suppose I conducted an analysis last year but only on the highest order grouping (groups A,B,C). So three models with 2 parameters each ($\beta_{0}$ and $\beta_{1}$) have been built. Now suppose I want to extend these models to include the subgroups. Can't I use the information gained from the first analysis? I thought that bayesian learning was exactly that: incorporate new insights to refine models, isn't that true? – Patrick Apr 17 at 16:08