In multinomial logistic regression, can I compare the categories that are not the reference category with each other? I am conducting multinomial log. regression, my DV has three categories, therefore my output gives me the comparison between the reference category and the other two. I would also like to compare those two which are not reference with each other. I know I can do this by changing the reference category in a second analysis, but are there problems associated with this? Thanks
 A: An easy way to find out whether or not the two models are equivalent is to predict probabilities. So fit your model with one category as the baseline and predict the probabilities for each category based on that model. Fit your model with another category as your baseline, and predict the probabilities for each category based on that second model. If the two sets of predicted probabilities are the same, then that is an indication that the models are equivalent. If you try this out, you'll see that that is the case. Below is an example of how I would do this in Stata:
sysuse auto, clear
recode rep78 1/2=3

// estimate a model with base category = 3
mlogit rep78 i.foreign mpg price
predict double Pr1*

// estimate a model with base category = 4    
mlogit rep78 i.foreign mpg price, base(4)
predict double Pr2*

// compare the predicted probabilities    
twoway function identiy = x ||                          ///
       scatter Pr11 Pr21    ||                          ///
       scatter Pr12 Pr22    ||                          ///
       scatter Pr13 Pr23, scheme(s2color)               ///
       legend(pos(4) cols(1)) ylab(,angle(horizontal))  ///
       ytitle("probabilities based on base category 4") ///
       xtitle("probabilities based on base category 3")


