Dear members of the list,

For a sample of highly educated young adults in 24 countries that participated in PIAAC survey, I estimate the probability of attaining a master level degree instead of a bachelor level one. Thus, my dependent variable is dichotomous. My key independent variable is father's education, which is a variable with three categories, corresponding to basic, intermediate and higher education. Controlling for gender and age, I want to estimate the effect of father's education on the attainment of a higher level degree (master) instead of a lower level one among the individuals in the sample. This is my model:

PHP Code:
xtmelogit univ i.edufath female age || cntryid3

In principle, my results show that father's education has an statistically significant effect on the probability of attaining a master level degree instead of a bachelor level one. See coefficients corresponding to ISCED 3/4 and ISCED 5/6 in the following table:

PHP Code:

Fitting comparison model
:

Iteration 0:   log likelihood = -12825.158  
Iteration 1
:   log likelihood =  -12512.74  
Iteration 2
:   log likelihood = -12511.102  
Iteration 3
:   log likelihood = -12511.102  

Fitting full model
:

tau =  0.0     log likelihood = -12511.102
tau 
=  0.1     log likelihood = -11306.365
tau 
=  0.2     log likelihood = -11278.014
tau 
=  0.3     log likelihood = -11276.239
tau 
=  0.4     log likelihood = -11317.484

Iteration 0
:   log likelihood =  -11258.67  
Iteration 1
:   log likelihood = -11162.029  
Iteration 2
:   log likelihood = -11153.553  
Iteration 3
:   log likelihood = -11153.329  
Iteration 4
:   log likelihood = -11153.329  

Random
-effects logistic regression              Number of obs     =     19,663
Group variable
cntryid3                        Number of groups  =         24

Random effects u_i 
Gaussian                   Obs per group:
                                                              
min =        320
                                                              avg 
=      819.3
                                                              max 
=      3,302

Integration method
mvaghermite                 Integration pts.  =         12

                                                Wald chi2
(4)      =     340.00
Log likelihood  
= -11153.329                    Prob chi2       =     0.0000

------------------------------------------------------------------------------
      
master |      Coef.   StdErr.      z    P>|z|     [95ConfInterval]
-------------+----------------------------------------------------------------
   
edufather |
  
ISCED 3/4  |   .1350686   .0466318     2.90   0.004     .0436719    .2264653
  ISCED 5
/6  |   .6315997   .0445544    14.18   0.000     .5442747    .7189247
             
|
      
female |  -.0768024   .0331973    -2.31   0.021    -.1418679    -.011737
         age 
|   .0336828    .003584     9.40   0.000     .0266582    .0407073
       _cons 
|  -2.447529   .3277209    -7.47   0.000     -3.08985   -1.805208
-------------+----------------------------------------------------------------
    /
lnsig2u |   .6325732    .304019                      .0367069    1.228439
-------------+----------------------------------------------------------------
     
sigma_u |   1.372023   .2085606                      1.018523    1.848214
         rho 
|   .3639468   .0703772                      .2397336    .5093969
------------------------------------------------------------------------------
LR test of rho=0chibar2(01) = 2715.55                Prob >= chibar2 0.000 

Next, I proceed to estimate the average marginal effect of different categories of father's education on the probability of attaining a master level degree instead of a bachelor one:

PHP Code:
margins edufatherpredict(mu fixedonlyvsquish level(95post
marginsplot 

I do not understand why, if the effect is statistically significant in the results (table above), the confidence intervals in the graph overlap. See next:

[ATTACH=CONFIG]temp_16427_1576179342494_40[/ATTACH]

Is there anyone who could help me to understand the correspondence between the statistical significance of the coefficients in the table and the overlap of the confidence intervals in the graph? Which one of these results should I credit?

Many thanks for your attention

Kind regards

Luis Ortiz