Non-centered parameterization for a hierarchical regression model

[hyang336]

Sorry for the potentially noob question. If I have a hierarchical regression model like v ~ 0 + x + y + (1|subID), how should I do non-centered parameterization?

[frankmj]

noncentered is an argument and is on by default in a hierarchical model. Though if you want the subID terms to be hierarchical you should either do: * v ~ 1+ x + y + (1|subID) that way the v_subID's will be offset from the group distribution which will be estimated as v_Intercept. without the "1" there is no group distribution from which the IDs will be offset. * If you want to use the v ~ 0 +... models and still do a hierarchical model you should actually set noncentered= false, but then use a hyperprior for the mean of the group distribution so that it can estimate the mu from which the subIDs are drawn. e.g.: in "prior": { "1|subID": {"name": "Normal", "mu": {"name": "Normal", "mu": 1, "sigma": 2}, "sigma": {"name": "HalfNormal", "sigma": 1, }, } The group distributions here will be estimated as v_1|subID_mu and the individual v's for each subject will be drawn from that centered distribution. * Also you might want to consider random slopes too if you want the model to be fully hierarchical v ~ 1 + x + y + (1+x+y|subID) for noncentered = true or v ~ 0+ (1+x+y|subID) for noncentered= false (and then you would set priors also for the x and y to come from the same hyperprior) Michael J Frank, PhD | Edgar L. Marston Professor Director, Carney Center for Computational Brain Science <https://www.brown.edu/carney/ccbs> Laboratory of Neural Computation and Cognition <https://www.lnccbrown.com/> Brown University website <http://ski.clps.brown.edu>

…

On Wed, Jun 19, 2024 at 11:40 AM hyang336 ***@***.***> wrote: Sorry for the potentially noob question. If I have a hierarchical regression model like v ~ 0 + x + y + (1|subID), how should I do non-centered parameterization? — Reply to this email directly, view it on GitHub <#465>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAG7TFG5XLXGFU3QCSE5AXLZIGQ5RAVCNFSM6AAAAABJSJ4LJKVHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZWHAZTSNBWHE> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>