Hi everyone,
I am running a model which has many interactions terms and I am facing difficulties in interpreting my results.
My dependent variable is the log of the hourly wage. The main covariates are female (1 if the respondent is female), vet_yes ( which is equal to one if the highest qualification of the individual is vocational qualification) and age which is a continuous variable (centered).
The main problem is that while I can easily understand where those coefficient come from when I don't include in the model the interaction between age squared and vet, once I include them I struggle to understand the meaning of those coefficients.

To compute the age slope for each combination of vet and gender I used:

margins, dydx(centered_age) over(female vet_yes)

Could someone advise me on how to interpret those results?

The following is my output:
log_trim_earnhrppp_cont_dcl Coef. Std. Err. t P>t [95% Conf. Interval]
1.female -.1833839 .0057791 -31.73 0.000 -.1947109 -.172057
1.vet_yes -.0471009 .0087654 -5.37 0.000 -.0642811 -.0299207
female#vet_yes
1 1 .0034801 .0078891 0.44 0.659 -.0119825 .0189428
centered_age .0101485 .0003907 25.98 0.000 .0093827 .0109142
female#c.centered_age
1 -.0032397 .0004942 -6.56 0.000 -.0042083 -.002271
vet_yes#c.centered_age
1 -.0035711 .0005128 -6.96 0.000 -.0045761 -.0025661
female#vet_yes#c.centered_age
1 1 .0030438 .0006858 4.44 0.000 .0016996 .004388
vet_yes#c.centered_age#c.centered_age
0 -.0005042 .0000218 -23.18 0.000 -.0005468 -.0004616
1 -.0002864 .0000212 -13.53 0.000 -.0003279 -.0002449
vetc .2781538 .0079748 34.88 0.000 .2625232 .2937844
vet_miss -.0026209 .0117015 -0.22 0.823 -.0255558 .020314
centered_numscore1 .0922938 .0026553 34.76 0.000 .0870893 .0974983
uni_degree .2847923 .0065771 43.30 0.000 .2719011 .2976834
prof_degree .1373752 .0065492 20.98 0.000 .1245387 .1502117
post_secondary .0633137 .0080403 7.87 0.000 .0475547 .0790727
med_upper_postsec .0336602 .0051705 6.51 0.000 .0235261 .0437943
med_unidegree .0302929 .0072227 4.19 0.000 .0161364 .0444494
med_miss -.0231609 .0147224 -1.57 0.116 -.0520169 .0056952
ded_upper_postsec .0255946 .0051962 4.93 0.000 .0154101 .0357791
ded_unidegree .0266815 .0068149 3.92 0.000 .0133242 .0400388
ded_miss -.0342802 .0119437 -2.87 0.004 -.0576899 -.0108705
books .0101725 .0017325 5.87 0.000 .0067769 .0135682
children .0292157 .0050228 5.82 0.000 .0193709 .0390605
daustria -.3231752 .0088421 -36.55 0.000 -.3405058 -.3058447
dczechrepublic -1.027535 .0137303 -74.84 0.000 -1.054446 -1.000624
destonia -.7824016 .0107683 -72.66 0.000 -.8035076 -.7612956
dfinland -.284851 .0075514 -37.72 0.000 -.2996518 -.2700501
dfrance -.4507601 .0079694 -56.56 0.000 -.4663802 -.4351399
dgermany -.3003515 .0102186 -29.39 0.000 -.3203801 -.280323
direland .1254127 .0123201 10.18 0.000 .1012653 .14956
djapan -.2922338 .0104464 -27.97 0.000 -.3127088 -.2717588
dkorea -.2558537 .0139317 -18.36 0.000 -.28316 -.2285475
dnetherlands -.1632647 .0094638 -17.25 0.000 -.1818137 -.1447157
dnorway -.012887 .0075659 -1.70 0.089 -.0277163 .0019423
dpoland -1.065299 .0123996 -85.91 0.000 -1.089602 -1.040995
dslovakrepublic -1.141286 .0119926 -95.17 0.000 -1.164792 -1.117781
dspain -.3037618 .0133448 -22.76 0.000 -.3299177 -.2776059
dsweden -.2408123 .0075793 -31.77 0.000 -.2556678 -.2259569
duk -.0637246 .0112755 -5.65 0.000 -.0858247 -.0416245
dusa .0634285 .0121456 5.22 0.000 .0396232 .0872339
_cons 2.847976 .0107049 266.04 0.000 2.826994 2.868957
Sincerely,
Maria