Interpretation of negative interaction term

[Sherine Maui]

I have two dummy variables that measure whether a woman has children and whether a woman has a son. They are both positively associated with my outcome variable, however, I get a negative moderating effect when I interact them.

From what I understand, when the interaction term is significant, the association between one of the predictors and the outcome variable decreases if the other predictor increases. In this case, would it be correct to then interpret this as - the association between having children and my outcome decreases if one already has a son?

Below is the output:

Linear regression                               Number of obs     =     11,267
                                                F(20, 21)         =          .
                                                Prob > F          =          .
                                                R-squared         =     0.0422
                                                Root MSE          =     1.4084

                                            (Std. Err. adjusted for 22 clusters in gov)
---------------------------------------------------------------------------------------
                      |               Robust
                   M1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
        1.dbirthstat2 |    .215039     .06759     3.18   0.004     .0744778    .3556002
          1.dsondum21 |   .7647043   .1263868     6.05   0.000     .5018687     1.02754
                      |
dbirthstat2#dsondum21 |
                 1 1  |  -.6213765   .1161624    -5.35   0.000    -.8629495   -.3798035
                      |
              qwealth |
                   2  |   .0502004   .0510862     0.98   0.337    -.0560391      .15644
                   3  |   -.022392   .0949086    -0.24   0.816    -.2197653    .1749813
                   4  |  -.1782484   .0887532    -2.01   0.058    -.3628208    .0063241
                   5  |  -.2621398   .1339137    -1.96   0.064    -.5406285     .016349
                      |
    dsondum21#qwealth |
                 1 2  |   -.118878    .068086    -1.75   0.095    -.2604706    .0227147
                 1 3  |  -.0519761   .0937919    -0.55   0.585     -.247027    .1430748
                 1 4  |  -.0008803   .0840967    -0.01   0.992    -.1757691    .1740084
                 1 5  |   .0537107     .09222     0.58   0.566    -.1380713    .2454928
                      |
            spercent2 |  -.0612342   .0620339    -0.99   0.335    -.1902407    .0677723
           totalchild |  -.0780945   .0159649    -4.89   0.000    -.1112952   -.0448938
               deduc2 |   .0464523   .0559993     0.83   0.416    -.0700046    .1629091
               deduc3 |   .1957602   .0536614     3.65   0.002     .0841653    .3073551
               deduc4 |   .1505687   .0675207     2.23   0.037     .0101518    .2909857
            dreleduc2 |   .1103587   .0480819     2.30   0.032     .0103669    .2103505
            dreleduc3 |   .0012099   .0459536     0.03   0.979    -.0943558    .0967756
            trousseau |   .0002523   .0025836     0.10   0.923    -.0051206    .0056251
         demployment2 |   .1913727   .0348394     5.49   0.000     .1189202    .2638251
               dyear2 |   .0139665   .0834786     0.17   0.869    -.1596367    .1875698
           dreligion1 |   .1679199    .066861     2.51   0.020     .0288748     .306965
              durban1 |   .1704622   .0730408     2.33   0.030     .0185654    .3223589
    dlivingstructure1 |  -.2129066    .084701    -2.51   0.020     -.389052   -.0367612
                  age |   .0545643   .0126246     4.32   0.000       .02831    .0808186
                      |
          c.age#c.age |  -.0004585    .000172    -2.67   0.014    -.0008163   -.0001008
                      |
        firstbirthage |  -.0109649   .0042524    -2.58   0.018    -.0198082   -.0021216
                 gdp1 |   .0032841   .0069749     0.47   0.643     -.011221    .0177892
                _cons |  -1.449096   .2671403    -5.42   0.000    -2.004645   -.8935477
---------------------------------------------------------------------------------------

.

Thanks.

[Carole J. Wilson]

If a woman has a son, doesn’t she, by definition, have children? Can she have a son, but no children?

I’ll disregard that for a moment. The negative interaction of two dummies with positive coefficients implies that having 1’s on both dummies has a smaller effect on the outcome than the sum of the individual effects of having 1’s on either. So, the effect of having a son is b1, the effect of having children is b2, but the effect of having both is b1+b2-b3.

[Sherine Maui]

Thank you for the explanation Carole. Yes I see your point, my justification for adding it was to see whether the 'effect' of having children is mainly due to having a son