polytomous regression - help obtaining p for heterogeneity

I am using polytomous (aka multinomial) logistic regression to analyze some data. My outcome/dependent variable is nominal (unordered) with 4 categories (0,1,2,3). Commonly in the literature I see tables where the adjusted odds ratios (OR) & 95% CI for the main predictor/independent variable are reported for each outcome (compared to referent) accompanied by a p-value in the final column.

My question is, how do I obtain this p-value?

It seems to commonly be described as "p for heterogeneity", "test for differences in ORs" or "test for equality of logits" and I think it comes from a wald test or likelihood ratio test. It is referred to in chapter 8 in Hosmer in Lemeshow Applied Logistic Regression but I can not figure it out.

I can tell from my overlapping CI's that my ORs are likely not signficantly different (and thus may justify pooling and the use of binary logistic regression) but it would be nice to be able to report the p-value.

I am currently using SAS (proc logistic with glogit function) but willing to run it in Stata or SPSS a try if anyone knows how.

Thanks in advance!


TS Contributor
I think this is the thing for my little simple model

if you got covariates itll be a little harder, but i hope this gets you
going in the right direction.

without covariates you can use this contrast statement to test equality of intercepts
(i think)

dm 'out; clear; log; clear;';

data X;
do i = 1 to 100;
Y = rand('table', 0.3,0.5,.2);
run; quit;

proc print data = X;
run; quit;

proc logistic data = X;
class x;
model Y = / link = glogit;
contrast 'x' intercepts 1 -1;

run; quit;