Adjusted Odds Ratio with Non-Significant P-Value but Significant Margins?

[Sara Sakowitz]

I am running a multivariable logistic regression and transforming the output into adjusted odds ratios. Here is the output:

Survey: Logistic regression

Number of strata   =       440                  Number of obs     =     22,438
Number of PSUs     =     5,411                  Population size   = 41,230.988
                                                Design df         =      4,971
                                                F(  52,   4920)   =      70.70
                                                Prob > F          =     0.0000

--------------------------------------------------------------------------------------------
                           |             Linearized
                     outcome_2 | Odds Ratio   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                     group |
                        0  |          1  (base)
                        1  |   1.720191   .2458567     3.80   0.000      1.29984    2.276478
                        2  |   1.169191   .1951802     0.94   0.349     .8428587    1.621872
                        3  |   1.178626    .181563     1.07   0.286     .8714046    1.594162
                        4  |   1.433473   .2405618     2.15   0.032     1.031593    1.991915

From this, I see that groups 2 and 3 have a P-Value >0.05.

However, I then run a margins, and see the following:

margins, by(i.group)

Predictive margins

Number of strata = 440 Number of obs = 22,438
Number of PSUs = 5,411 Population size = 41,230.988
Model VCE : Linearized Design df = 4,971

Expression : Pr(outcome_2), predict()
over : group

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
group|
0 | .4901843 .003289 149.04 0.000 .4837364 .4966322
1 | .6628769 .0241366 27.46 0.000 .6155586 .7101953
2 | .6034503 .0286592 21.06 0.000 .5472656 .659635
3 | .557703 .0278401 20.03 0.000 .5031241 .6122819
4 | .5940185 .0291992 20.34 0.000 .5367752 .6512619
------------------------------------------------------------------------------

What does it mean, that my AOR has a non-significant P-value with the base group (group=0) as reference, yet when I look at the confidence intervals in the post-estimation margins, there is no overlap?

I am confused how to interpret this, and would appreciate any guidance. My sample is small in groups 1-4, could that skew the margins estimation? Thank you so much.

[Leonardo Guizzetti]

All margins is reporting to you is the marginal mean predicted probability of your outcome. The tests associated with each one have the null hypothesis that the mean is 0, which is not scientifically or otherwise interesting.

[Sara Sakowitz]

I see- to compare them with each other, would I have to do a contrast? Thank you so much!

[Leonardo Guizzetti]

You could use test or testparm to work directly with the model coefficients since that is probably what you want.
lincom is another way to specific linear combinations and contrasts of three coefficients.
You have to give us more detail if you want a more specific answer.