I ran multinomial logit model (code below). Dependent variableis gender (M, F, Unknown). Model has one independent variable for the year, which I have coded as 1, 2, 3, 4, etc. (so is continuous in the model). Clustered standard errors are used as the same person can be found in multiple years. Analysis question: are there statistically significant trends over time in % males, % females, % unknown.

Question: can one determine if there are statistically significant differences in predicted probabilities after mlogit? I found some code after a cmclogit example (and adjusted it a bit) so am not sure if it works for mlogit.

1. For the code below, does the (2 vs 1, p<0.001) for example tell us if expected probability of being F (outcome =1) is statistically significantly higher in year 2 v year 1?

Code:

. margins, at(year = (2008(1)2013)) predict(outcome(1)) contrast(atcontrast(ar) nowald effects)

Contrasts of adjusted predictions
Model VCE    : Robust

Expression   : Pr(gender_n==Female), predict(outcome(1))

1._at        : year            =        2008

2._at        : year            =        2009

3._at        : year            =        2010

4._at        : year            =        2011

5._at        : year            =        2012

6._at        : year            =        2013

------------------------------------------------------------------------------
             |            Delta-method
             |   Contrast   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
   (2 vs 1)  |   .0103146   .0015862     6.50   0.000     .0072056    .0134235
   (3 vs 2)  |   .0106397    .001709     6.23   0.000     .0072901    .0139892
   (4 vs 3)  |   .0109603   .0018311     5.99   0.000     .0073715    .0145491
   (5 vs 4)  |   .0112751   .0019515     5.78   0.000     .0074503    .0150999
   (6 vs 5)  |   .0115829   .0020691     5.60   0.000     .0075275    .0156383
------------------------------------------------------------------------------
2. can we test whether there is a statistically significant difference in the expected probabilities of male and female when the year = 2013? Code below gives the error: option outcome() not allowed r(198);
Code:
  . margins, at(year=2013) outcome((1 2)) contrast(outcomecontrast(r) nowald effects)
Note: I am using Stata 15.

Code for original model below, FYI.

Code:
. mlogit gender_n year, rrr vce(cluster person)

Iteration 0:   log pseudolikelihood = -14352.761  
Iteration 1:   log pseudolikelihood = -14333.167  
Iteration 2:   log pseudolikelihood = -14333.146  
Iteration 3:   log pseudolikelihood = -14333.146  

Multinomial logistic regression                 Number of obs     =     17,035
                                                Wald chi2(2)      =      51.85
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -14333.146               Pseudo R2         =     0.0014

                             (Std. Err. adjusted for 8,124 clusters in person)
------------------------------------------------------------------------------
             |               Robust
    gender_n |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Female       |
        year |   1.056973   .0110526     5.30   0.000     1.035531    1.078859
       _cons |   1.44e-49   3.02e-48    -5.35   0.000     1.83e-67    1.12e-31
-------------+----------------------------------------------------------------
Male         |  (base outcome)
-------------+----------------------------------------------------------------
U            |
        year |    .952431   .0124788    -3.72   0.000     .9282843    .9772059
       _cons |   5.53e+41   1.46e+43     3.65   0.000     2.14e+19    1.43e+64
------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.