# Comparing regression coefficients across groups in multinomial logistic regression

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.