st: prtab/prvalue: compare predicted probabilities across values of X

["Yam, Eileen A." <eyam@jhsph.edu>]

I am running a multinomial logistic regression (for a four-value outcome 'conmix') and I would like to assess whether predicted probabilities for each of the four possible outcomes vary across four age categories ('agecat4'). I understand how to estimate the predicted probabilities themselves, but if I would like to test whether those predicted probabilities for a given outcome are significantly different across age categories, what is the most efficient way to do this?

So far, I've done:

quietly xi:mlogit conmix i.zone i.agecat4 i.kidscat i.educat2 i.inc_cat  prevhiv i.i_newmocat i.i_regmocat i.part_mocat anycondfail, base(0) rrr
prvalue, x(_Iagecat4_2==0 _Iagecat4_3==0 _Iagecat4_4==0)
prvalue, x(_Iagecat4_2==1)
prvalue, x(_Iagecat4_3==1)
prvalue, x(_Iagecat4_4==1)

This gives me the predicted probability of each of the four outcomes within each of the four age categories. But how can I test for whether the predicted probabilities are significantly different across age categories?
 For example, if I wanted to say that the predicted probability of outcome 1 was significantly different across all age categories (i.e., a global test), how would I test this? 
Then, if I wanted to say that the predicted probability of outcome 1 was higher for age category 1 compared to age category 2, how would I test this?

Many thanks, 
Eileen
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