Statistical significance different: predicted probability vs average marginal effect differences

[Sarah Thea Smith]

I am currently writing up some of my findings (based on multiply imputed data) and have noticed some discrepancies in the statistical significance I find:

When using the below code to calculate differences in average marginal effects of two binary variables, I do not find a statistically significant difference...

mimrgns x1, dydx(x2) predict(pr) pwcompare

...but I do find one when calculating differences in predicted probabilities (even when looking at 99% CIs) using the below code:

mimrgns i.x1##i.x2, predict(pr) pwcompare

To add to this, I do find a statistically significant difference when looking at the log-odds in the regression table.

I am therefore wondering which indicator of statistical significance I should focus on; i.e. can I conclude there are statistically significant group differences based on the comparison of predicted probabilities (and the log-odds), or should I conclude I do not find statistically significant differences based on the AMEs?

[Sarah Thea Smith]

Update: I figured out that I was comparing incorrect numbers, the AME value refers to the difference between two category differences calculated using the predicted probability code.

I would still be interested in anyone's opinion regarding differences in the effect direction and statistical significance when comparing log-odds and AMEs though!