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I'm attempting to form a Bayesian Hierarchical Regression Model and one of my regressors is for an indicator variable. My hierarchy structure has separate group-level regressors related across-groups by the assumption that these regressors are drawn from a common distribution. For one of the base-level groups I'm considering, all of the values for that group corresponding to the indicator variable are zeros. As this will be problematic given that this will result in rank-deficient matrices, what, if anything, can be done in this case? Am I forced to drop the variable?

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  • $\begingroup$ If they're the only ones with 0's for the indicator, they'd be the group comprising your baseline level for that indicator. If you have multiple groups that you're interested in differences between who all have some zeros in the indicator, then it sounds like your design has confounded the group differences (vs that group) with the indicator, and normally you'd drop either the indicator or the group... though it's possible I've misunderdstood something about your description. $\endgroup$
    – Glen_b
    Commented Jul 4, 2015 at 2:29
  • $\begingroup$ @Glen_b So far this is the only group that has 0's for that indicator, but there may be others. I'm trying to test my model with a subset of my data before I utilize all of it. What I'm trying to measure is the effect of the indicator variable on my dependent variable. I had looked up this other source on Hierarchical Bayesian Regression [twiecki.github.io/blog/2014/03/17/bayesian-glms-3/], which only used an indicator in its regression so I assumed that it wouldn't be problematic. It looks like you're understanding what I'm describing though. $\endgroup$
    – TSP
    Commented Jul 4, 2015 at 2:43
  • $\begingroup$ So if you don't also have indicators for your group membership (your model treats the group as not being relevant to the response), then any confounding between group and this indicator won't matter. However, this does concern me that there's something I haven't understood about the situation -- for example, if you only have one indicator variable, how are you creating a hierarchical model? $\endgroup$
    – Glen_b
    Commented Jul 4, 2015 at 2:48
  • $\begingroup$ @Glen_b Exactly as you said. This indicator doesn't imply group membership. I'm trying to create a partial-pooled model so that each group has separate regressors but the regressors are drawn from a distribution with a common mean. The source I'm consulting refers to this as a hierarchical regression model. Is that correct? $\endgroup$
    – TSP
    Commented Jul 4, 2015 at 3:09
  • $\begingroup$ Sorry, I didn't follow your description there. Perhaps you could clarify the situation you're in (in some detail) in your question? It might help people give helpful answers $\endgroup$
    – Glen_b
    Commented Jul 4, 2015 at 3:11

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