Suppose that I fit a Bayesian multinomial logistic regression model where the dependent categorial variable indexes $x$ groups, and the predictors are the same across groups. I now have $x - 1$ sets of $p$ regression coefficients and want to compare the regression coefficients of one of the groups to the two others. One simple ad hoc way to do this is to compare the posterior distributions of the coefficients. But I'm sure there is a better way. Thanks.
It's not quite clear to me how you've set things up, but I have a feeling that you've bumped into this problem in which case the different sets of coefficients are not necessarily comparable at all without extra assumptions about the unobserved heterogeneity.