Interpretation r.a#r.b interaction (margins command)

[Lydia Palumbo]

Dear Statalisters,

I ran the following logit model and then computed the marginal effects of my variable of interest in this way.

svy, subpop(if marital==1&age>17&age<35) : logit event1 ib0.skills##i.agesm i.sex  i.educ2  i.wave5  i.biosonsn2 i.london ib1.nssecpar  i.religion3 i.ethnicity, or level(95)

margins r(0 1 2 )b0.skills, level(95) atmeans  post  at(agesm=(0(1)3)) subpop(if marital==1&age>17&age<35)  noatleg

In this way, I obtain the differences in the predicted probabilities in each age group between levels 1, 2 and 3 and the reference one 0.

Now I would like to understand whether the differences that I obtained are signficantly different from one reference age group (18-21). I want to test it formally. I am using this code:

collect : margins r(1 2 3).skills#r.agesm, level(95) atmeans post subpop(if marital==1&age>17&age<36&(evunion==2)&jbstat!=7&iv fioall==1&save_new<2&skills<5&contr3<3&tercile3<3& means_benefits22<3&finnow3<2&finfut<4&tenure3<4&in du!=1) saving(skills, replace)

obtain this output

                                                                                 Delta-method
                                                                Contrast    std. err.    [95% conf.    interval]
                                
 skills#agesm    
(Routine    vs    Non-routine)            (22–24 vs 18–21)     -.0075323    .0154369    -.0377924    .0227279
(Routine    vs    Non-routine)            (25–29 vs 18–21)     -.0269329    .0165922    -.0594576    .0055919
(Routine    vs    Non-routine)            (30–34 vs 18–21)     .0189692     .0197626    -.0197703    .0577088
(Not    employed    vs    Non-routine)    (22–24 vs 18–21)     -.0767736    .0162389    -.1086059    -.0449413
(Not    employed    vs    Non-routine)    (25–29 vs 18–21)     -.0604068    .0207514    -.1010845    -.0197292
(Not    employed    vs    Non-routine)    (30–34 vs 18–21)     -.0243907    .018812    -.0612668    .0124853

I interpret the fourth line saying that "The differences in the probability of Y between not employed and non-routine are signficantly greater among those aged 22-24 than among those aged 18-21". In sum, this means that the marginal effects of not employed vs. non-routine increase with age.

I would like to know if I interpret this in the correct way.
Thank you.
Lydia