Hi all, I produced the below plot of predicted probabilities after running mlogit (full code below). Questions:

1) In 2013 (for example), the 95% CIs for M, F, and U do not overlap. Can I therefore conclude that the expected probabilities are statistically significantly different (at 5% level) for these 3 groups?

2) For the F group the CIs do not overlap for 2013 v 2008. Can I conclude the predicted probabilities are statistically significant (5% level) for those 2 years?

I understand if the CIs do overlap, they may or may not be statistically significantly different.



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

Iteration 0:   log pseudolikelihood = -10918.203  
Iteration 1:   log pseudolikelihood = -10906.418  
Iteration 2:   log pseudolikelihood = -10906.402  
Iteration 3:   log pseudolikelihood = -10906.402  

Multinomial logistic regression                 Number of obs     =     12,899
                                                Wald chi2(2)      =      33.46
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -10906.402               Pseudo R2         =     0.0011

                             (Std. Err. adjusted for 7,014 clusters in person)
------------------------------------------------------------------------------
             |               Robust
    gender_n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Female       |
        year |    .048562   .0143528     3.38   0.001      .020431    .0766931
       _cons |  -98.68828   28.86279    -3.42   0.001    -155.2583   -42.11825
-------------+----------------------------------------------------------------
Male         |  (base outcome)
-------------+----------------------------------------------------------------
U            |
        year |  -.0724472   .0184879    -3.92   0.000    -.1086829   -.0362116
       _cons |   143.8082   37.17114     3.87   0.000     70.95414    216.6623
------------------------------------------------------------------------------

. margins, at(year = (2008(1)2013))

Adjusted predictions                            Number of obs     =     12,899
Model VCE    : Robust

1._predict   : Pr(gender_n==Female), predict(pr outcome(1))
2._predict   : Pr(gender_n==Male), predict(pr outcome(2))
3._predict   : Pr(gender_n==U), predict(pr outcome(3))

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
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_predict#_at |
        1 1  |   .2060591   .0085704    24.04   0.000     .1892615    .2228567
        1 2  |   .2160034   .0071416    30.25   0.000     .2020061    .2300007
        1 3  |    .226174   .0060819    37.19   0.000     .2142537    .2380943
        1 4  |   .2365643   .0058009    40.78   0.000     .2251948    .2479338
        1 5  |   .2471675   .0065827    37.55   0.000     .2342657    .2600693
        1 6  |   .2579761   .0082736    31.18   0.000     .2417602     .274192
        2 1  |   .6677101   .0101316    65.90   0.000     .6478526    .6875676
        2 2  |   .6667553   .0082352    80.96   0.000     .6506146    .6828961
        2 3  |   .6650561   .0069231    96.06   0.000     .6514871    .6786251
        2 4  |   .6626354   .0065492   101.18   0.000     .6497993    .6754715
        2 5  |   .6595178   .0072932    90.43   0.000     .6452235    .6738121
        2 6  |   .6557291   .0089327    73.41   0.000     .6382213    .6732369
        3 1  |   .1262308   .0073137    17.26   0.000     .1118962    .1405653
        3 2  |   .1172412   .0057115    20.53   0.000     .1060469    .1284355
        3 3  |   .1087699   .0046996    23.14   0.000     .0995588     .117981
        3 4  |   .1008003   .0043574    23.13   0.000     .0922599    .1093406
        3 5  |   .0933147   .0045779    20.38   0.000     .0843422    .1022873
        3 6  |   .0862948   .0051102    16.89   0.000     .0762791    .0963105
------------------------------------------------------------------------------

. marginsplot

  Variables that uniquely identify margins: year _outcome
Array