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How does one interpret the beta coefficients in R for a model that has a categorical dependent variable that is not binary? For instance, in the hypothetical model below, I would interpret B1 as being both statistically significant and positive, but if my categorical dependent variable can take on 4 categories, then which category does B1 positively predict? That is, if the DV can be (blue, red, green, yellow), what does B1 predict?

As an side, I am dealing with a very small sample size.

   bayesglm(formula = DV ~ B1 + B2 + B3, family = binomial(link = "probit"), 
    data = data)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.07714   0.03221   0.14180   0.25680   0.86569  

Coefficients:
                             Estimate Std. Error z value Pr(>|z|)  
(Intercept)                -6.336e-01  1.859e+00  -0.341   0.7332  
B1                          2.691e+00  1.347e+00   1.998   0.0457 *
B2                          1.586e+00  1.297e+00   1.223   0.2212  
B3                          6.637e-01  1.755e+00   0.378   0.7052
stat_novice
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    I don't know anything about `bayesglm` per se, but I suspect it is just a multinomial logistic regression from a Bayesian perspective rather than a frequentist one. If so, the interpretations of the betas would be more or less the same, & this thread: [interpreting-exp(b)-in-multinomial-logistic-regression](http://stats.stackexchange.com/questions/17196/) should help you. – gung - Reinstate Monica Nov 09 '13 at 21:44
  • @Gung Thank you, but that thread doesn't address my question. Bayesglm is similar to glm, except for the fact it includes a penalty to help deal with collinearity. – stat_novice Nov 09 '13 at 22:03
  • `bayesglm` is a wrapper around `glm` so cannot fit any model that `glm` cannot fit. So what you have estimated is a usual, binary logistic regression. You probably want multinomial logistic regression. Search this site. – kjetil b halvorsen Jul 20 '19 at 17:19

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