Possibly a rudimentary question, but I am unsure how my interaction is behaving this way. When I use the following code,
Code:
 logit vaccinated male age ib0.race_rc native ib1.marstat numchild h14hhres proxy  work insurance  ib1.wealthquint1 ib0.cenreg masks_toomuch malechild  reduccat##keducat, or allbaselevels
I receive the following output
Code:
. logit vaccinated male age ib0.race_rc native ib1.marstat numchild h14hhres proxy  work insurance  ib1.wealthquint1 ib0.cenreg masks_toomuch malechild  reduccat##keducat, or allbaselevels

Iteration 0:   log likelihood = -1695.4695  
Iteration 1:   log likelihood = -1512.5555  
Iteration 2:   log likelihood = -1487.5511  
Iteration 3:   log likelihood =   -1487.39  
Iteration 4:   log likelihood =   -1487.39  

Logistic regression                                     Number of obs =  4,225
                                                        LR chi2(31)   = 416.16
                                                        Prob > chi2   = 0.0000
Log likelihood = -1487.39                               Pseudo R2     = 0.1227

------------------------------------------------------------------------------------
        vaccinated | Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
-------------------+----------------------------------------------------------------
              male |   1.194619   .1258765     1.69   0.091     .9717147    1.468657
               age |   1.032606   .0068076     4.87   0.000     1.019349    1.046035
                   |
           race_rc |
         NH-White  |          1  (base)
         NH-Black  |   1.482211   .2115324     2.76   0.006     1.120551    1.960598
         NH-Other  |   .6913389   .1741085    -1.47   0.143     .4220095    1.132556
         Hispanic  |   2.474591   .5055626     4.43   0.000     1.658065     3.69322
                   |
            native |   .6683936   .1335477    -2.02   0.044      .451813    .9887939
                   |
           marstat |
          Married  |          1  (base)
      Sep/Divorce  |   .6733267   .0915843    -2.91   0.004     .5157598     .879031
          Widowed  |   .4842703   .0656398    -5.35   0.000     .3712896    .6316301
    Never-married  |   .8865486   .2507104    -0.43   0.670      .509317    1.543181
                   |
          numchild |   .9417637   .0249689    -2.26   0.024     .8940753    .9919957
          h14hhres |   .9002094   .0360627    -2.62   0.009     .8322315    .9737398
             proxy |   .2817702    .082959    -4.30   0.000     .1582282    .5017721
              work |   .9485741   .1070232    -0.47   0.640     .7603861    1.183337
         insurance |   1.623376   .3575462     2.20   0.028     1.054249    2.499741
                   |
      wealthquint1 |
                1  |          1  (base)
                2  |   1.166197   .1657533     1.08   0.279     .8826515    1.540829
                3  |   1.137073   .1702812     0.86   0.391     .8478471    1.524963
                4  |   1.289984   .2071102     1.59   0.113       .94172    1.767042
                5  |   2.729461   .5490092     4.99   0.000     1.840198    4.048454
                   |
            cenreg |
               NE  |          1  (base)
               MW  |   .6457031   .1185107    -2.38   0.017     .4506149    .9252525
            South  |   .4683402    .080053    -4.44   0.000     .3350166    .6547215
             West  |   .5105215   .0963674    -3.56   0.000     .3526461     .739076
                   |
     masks_toomuch |   .2888079    .030219   -11.87   0.000     .2352583    .3545465
         malechild |   .9438558   .0907005    -0.60   0.548     .7818237    1.139469
                   |
          reduccat |
               HS  |          1  (base)
         Some Col  |   1.199936   .3153607     0.69   0.488     .7168853    2.008474
             Col+  |   1.658133    .775249     1.08   0.279     .6632017    4.145653
                   |
           keducat |
               HS  |          1  (base)
         Some Col  |   1.021394   .1725488     0.13   0.900     .7334933    1.422299
             Col+  |    1.68241    .279711     3.13   0.002     1.214547    2.330501
                   |
  reduccat#keducat |
            HS#HS  |          1  (base)
      HS#Some Col  |          1  (base)
          HS#Col+  |          1  (base)
      Some Col#HS  |          1  (base)
Some Col#Some Col  |   .8684592   .2829902    -0.43   0.665     .4585458    1.644812
    Some Col#Col+  |   .8416305   .2599964    -0.56   0.577      .459376    1.541965
          Col+#HS  |          1  (base)
    Col+#Some Col  |   .8178248   .4299102    -0.38   0.702     .2918802    2.291479
        Col+#Col+  |   .7731643    .382879    -0.52   0.603     .2929193    2.040778
                   |
             _cons |   1.207807   .7189185     0.32   0.751     .3761315    3.878422
------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.
I have multiple omitted categories. I am attempting to interaction respondent's education (HS, some college, college) with their child's education (HS, some college, college). How do I interpret my coefficients? Is plotting necessary, if so, a margins plot?

Part of my confusion is that when I run the code with only the interaction and no main effects, I receive output that I would expect. What is the correct approach and why is there a difference?

Code:
logit vaccinated male age ib0.race_rc native ib1.marstat numchild h14hhres proxy  work insurance  ib1.wealthquint1 ib0.cenreg masks_toomuch malechild  reduccat#keducat, or allbaselevels
Code:
. logit vaccinated male age ib0.race_rc native ib1.marstat numchild h14hhres proxy  work insurance  ib1.wealthquint1 ib0.cenreg masks_toomuch malechild  reduccat#keducat, or allbaselevels

Iteration 0:   log likelihood = -1695.4695  
Iteration 1:   log likelihood = -1512.5555  
Iteration 2:   log likelihood = -1487.5511  
Iteration 3:   log likelihood =   -1487.39  
Iteration 4:   log likelihood =   -1487.39  

Logistic regression                                     Number of obs =  4,225
                                                        LR chi2(31)   = 416.16
                                                        Prob > chi2   = 0.0000
Log likelihood = -1487.39                               Pseudo R2     = 0.1227

------------------------------------------------------------------------------------
        vaccinated | Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
-------------------+----------------------------------------------------------------
              male |   1.194619   .1258765     1.69   0.091     .9717147    1.468657
               age |   1.032606   .0068076     4.87   0.000     1.019349    1.046035
                   |
           race_rc |
         NH-White  |          1  (base)
         NH-Black  |   1.482211   .2115324     2.76   0.006     1.120551    1.960598
         NH-Other  |   .6913389   .1741085    -1.47   0.143     .4220095    1.132556
         Hispanic  |   2.474591   .5055626     4.43   0.000     1.658065     3.69322
                   |
            native |   .6683936   .1335477    -2.02   0.044      .451813    .9887939
                   |
           marstat |
          Married  |          1  (base)
      Sep/Divorce  |   .6733267   .0915843    -2.91   0.004     .5157598     .879031
          Widowed  |   .4842703   .0656398    -5.35   0.000     .3712896    .6316301
    Never-married  |   .8865486   .2507104    -0.43   0.670      .509317    1.543181
                   |
          numchild |   .9417637   .0249689    -2.26   0.024     .8940753    .9919957
          h14hhres |   .9002094   .0360627    -2.62   0.009     .8322315    .9737398
             proxy |   .2817702    .082959    -4.30   0.000     .1582282    .5017721
              work |   .9485741   .1070232    -0.47   0.640     .7603861    1.183337
         insurance |   1.623376   .3575462     2.20   0.028     1.054249    2.499741
                   |
      wealthquint1 |
                1  |          1  (base)
                2  |   1.166197   .1657533     1.08   0.279     .8826515    1.540829
                3  |   1.137073   .1702812     0.86   0.391     .8478471    1.524963
                4  |   1.289984   .2071102     1.59   0.113       .94172    1.767042
                5  |   2.729461   .5490092     4.99   0.000     1.840198    4.048454
                   |
            cenreg |
               NE  |          1  (base)
               MW  |   .6457031   .1185107    -2.38   0.017     .4506149    .9252525
            South  |   .4683402    .080053    -4.44   0.000     .3350166    .6547215
             West  |   .5105215   .0963674    -3.56   0.000     .3526461     .739076
                   |
     masks_toomuch |   .2888079    .030219   -11.87   0.000     .2352583    .3545465
         malechild |   .9438558   .0907005    -0.60   0.548     .7818237    1.139469
                   |
  reduccat#keducat |
            HS#HS  |          1  (base)
      HS#Some Col  |   1.021394   .1725488     0.13   0.900     .7334933    1.422299
          HS#Col+  |    1.68241    .279711     3.13   0.002     1.214547    2.330501
      Some Col#HS  |   1.199936   .3153607     0.69   0.488     .7168853    2.008474
Some Col#Some Col  |    1.06439   .2106292     0.32   0.753     .7222025     1.56871
    Some Col#Col+  |   1.699069   .3044057     2.96   0.003     1.195941    2.413863
          Col+#HS  |   1.658133    .775249     1.08   0.279     .6632017    4.145653
    Col+#Some Col  |   1.385074   .3465041     1.30   0.193     .8482579    2.261612
        Col+#Col+  |   2.156864   .4052279     4.09   0.000     1.492453     3.11706
                   |
             _cons |   1.207807   .7189185     0.32   0.751     .3761315    3.878422
------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.


Example data

Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input byte(vaccinated male) float(age race_rc) double(native marstat) byte(numchild h14hhres) double proxy byte work float insurance byte(wealthquint1 cenreg masks_toomuch malechild)
1 0 75 0 1 2 2 2 0 0 1 5 0 0 1
1 0 74 0 1 2 1 1 0 0 1 5 0 0 0
1 1 85 0 1 1 2 2 0 0 1 5 0 0 0
1 0 78 0 1 1 2 2 0 0 1 5 0 0 0
1 0 86 0 1 1 3 2 0 0 1 5 0 0 1
1 0 86 1 1 4 2 1 0 0 1 1 0 0 1
0 0 82 0 0 3 3 5 0 0 1 4 0 0 0
1 0 83 2 0 1 3 2 0 0 1 4 3 1 0
1 1 81 2 0 1 3 2 0 0 1 4 3 0 0
1 1 81 0 1 1 1 2 0 0 1 4 3 0 1
1 0 81 0 1 1 1 2 0 0 1 4 3 0 1
1 0 81 1 0 3 4 1 0 0 1 3 0 0 1
1 0 74 1 1 3 5 4 0 1 1 1 2 0 1
1 1 83 3 1 1 . 2 0 0 1 4 3 0 1
1 0 72 0 1 1 . 2 0 0 1 4 3 0 1
1 1 85 0 1 1 4 6 0 0 1 4 3 1 0
1 0 80 0 1 1 4 6 0 1 1 4 3 0 0
1 1 89 0 0 1 5 2 0 0 1 5 3 1 1
0 0 82 1 1 4 1 1 0 1 1 1 3 0 0
1 0 82 0 1 3 3 2 0 0 1 3 2 0 1
1 0 81 0 0 2 2 1 0 0 1 3 1 0 0
1 0 87 0 1 3 4 1 0 0 1 5 1 0 1
0 0 84 0 1 . . . . . . . . 0 0
1 1 81 0 1 3 5 2 0 1 1 5 1 0 1
0 0 91 0 1 3 3 5 1 0 1 4 1 0 0
1 0 90 0 1 3 4 2 0 0 1 3 1 0 1
1 1 87 1 1 1 4 2 0 1 1 3 3 0 1
1 0 65 1 1 1 . . . . . . . 0 1
1 1 84 0 1 1 3 2 0 0 1 2 2 0 1
1 0 80 0 1 3 5 1 0 0 1 1 2 0 0
1 0 89 0 1 1 4 2 0 0 1 4 1 0 1
1 0 85 1 1 3 8 1 0 0 1 1 1 0 0
1 0 82 1 0 1 1 3 0 0 1 2 1 0 0
1 1 85 2 1 1 1 3 0 1 . 2 1 0 0
1 0 80 0 1 1 5 2 0 0 1 2 1 1 0
1 1 84 0 1 1 2 2 0 0 1 3 1 0 0
1 0 78 0 1 1 2 2 0 0 1 3 1 0 0
1 0 89 0 1 3 4 3 0 0 1 3 1 0 1
1 0 80 0 1 2 1 1 0 0 1 3 1 1 0
1 0 90 1 1 3 2 1 0 1 1 3 1 0 0
1 0 76 1 1 3 3 1 0 0 1 1 1 0 0
1 0 85 1 1 3 4 1 0 0 1 1 1 0 1
1 0 83 1 1 3 2 1 0 0 1 1 1 0 0
1 0 68 0 1 3 1 1 0 0 1 5 3 0 1
1 1 84 0 1 1 2 2 0 0 . 4 3 . 1
1 0 78 0 1 1 2 2 0 0 1 4 3 0 1
0 0 84 0 1 3 7 2 0 0 1 5 3 1 1
1 0 90 0 1 1 2 2 0 0 1 2 3 0 1
1 1 90 0 1 1 2 2 0 0 1 2 3 0 1
0 0 66 1 1 3 . 1 0 0 1 1 3 0 1
1 1 81 1 1 1 4 2 0 0 1 4 3 0 1
1 0 71 1 1 1 4 2 0 0 1 4 3 0 1
1 0 65 1 1 2 2 1 0 1 1 1 2 0 1
1 0 86 1 1 2 3 2 0 0 0 3 2 0 0
1 0 86 0 1 3 3 1 0 0 1 3 2 0 0
1 0 80 1 1 2 3 2 0 1 1 3 2 0 1
1 0 90 0 1 1 2 2 0 0 1 3 2 0 1
1 1 82 1 1 2 2 1 0 0 1 4 2 0 0
1 0 83 0 1 3 3 3 0 0 1 3 2 0 0
0 0 74 0 1 2 2 3 0 0 1 5 2 1 0
1 1 87 0 1 1 3 2 0 0 1 3 2 1 1
1 0 75 0 1 1 3 2 0 0 1 3 2 0 1
1 1 80 1 1 3 1 1 0 0 1 2 2 0 1
1 0 72 1 1 3 2 2 0 0 1 2 2 0 1
1 0 80 0 1 . . . . . . . . 1 0
1 0 79 1 1 3 3 1 0 0 1 3 2 0 0
1 0 77 0 1 1 2 2 0 0 1 5 0 0 1
1 0 80 0 1 2 2 1 0 0 1 5 0 0 0
0 0 95 0 1 3 3 1 0 0 1 4 0 0 0
1 0 75 3 0 3 5 1 0 0 1 1 0 0 0
1 0 84 0 1 3 1 1 0 1 1 4 0 0 1
1 1 82 3 0 1 1 2 0 0 1 3 2 0 0
1 0 84 3 0 1 1 2 0 0 1 3 2 0 0
1 1 90 0 1 3 4 6 0 0 1 4 3 0 1
1 0 86 0 1 3 7 1 0 0 1 5 1 0 0
1 0 78 0 1 . . . . . . . . 0 1
1 0 77 0 1 3 4 2 0 0 1 5 1 0 1
0 1 87 0 1 1 3 2 0 0 1 2 1 0 1
0 0 87 0 1 1 3 2 0 0 1 2 1 0 1
1 1 82 0 1 1 2 2 0 0 1 4 0 0 1
1 0 80 0 1 1 2 2 0 0 1 4 0 . 1
1 1 87 0 1 1 3 2 0 0 1 4 0 0 1
1 0 86 0 1 1 3 2 0 0 1 4 0 0 1
1 1 80 0 1 1 2 2 0 1 1 4 0 0 1
1 0 77 0 1 1 2 2 0 0 1 4 0 0 1
1 1 92 0 1 2 3 1 0 0 1 2 2 0 0
1 0 87 0 1 3 2 2 0 0 1 3 0 0 1
1 0 82 0 1 3 4 1 0 0 1 2 0 0 1
1 1 80 0 1 1 4 2 0 0 1 4 0 0 1
1 0 79 0 1 1 4 2 0 0 1 4 0 1 1
1 1 82 0 1 1 2 2 0 0 1 5 2 0 0
1 0 77 0 1 1 2 2 0 1 1 5 2 0 0
1 0 93 1 1 . . . . . . . . 1 1
1 0 82 1 1 3 6 4 0 0 1 2 2 0 1
1 1 84 0 1 3 3 1 0 0 1 2 2 0 0
1 0 76 0 1 3 3 2 0 0 1 5 0 0 1
1 0 80 0 1 2 2 3 0 0 1 2 2 0 0
1 1 90 1 1 . . . . . . . . 1 1
1 1 83 0 1 1 3 2 0 0 1 5 1 0 0
1 0 82 0 1 1 3 2 0 0 1 5 1 0 0
end
label values race_rc race
label def race 0 "NH-White", modify
label def race 1 "NH-Black", modify
label def race 2 "NH-Other", modify
label def race 3 "Hispanic", modify
label values marstat mar
label def mar 1 "Married", modify
label def mar 2 "Sep/Divorce", modify
label def mar 3 "Widowed", modify
label def mar 4 "Never-married", modify
label values cenreg cen
label def cen 0 "NE", modify
label def cen 1 "MW", modify
label def cen 2 "South", modify
label def cen 3 "West", modify