ols interactions (is the effect of age on seius different for male and female?)

[Ayorinde Ogunyiola]

Clyde Schechter

is the effect of age on seius different for male and female?


reg seius i.female##c.age


margins female

margins, at(age=(20(10)60))


margins female, at(age=(20(10)60))

margins, dydx(female) at(age=(20(10)60))


reg seius i.female##c.age

Source SS df MS Number of obs = 1148
F( 3, 1144) = 3.71
Model 1273.17883 3 424.392942 Prob > F = 0.0114
Residual 131023.563 1144 114.531087 R-squared = 0.0096
Adj R-squared = 0.0070
Total 132296.742 1147 115.341536 Root MSE = 10.702


seius Coef. Std. Err. t P>t [95% Conf. Interval]

1.female 1.11425 2.131621 0.52 0.601 -3.068075 5.296576
age .1177876 .0480567 2.45 0.014 .0234984 .2120768

female#c.age
1 -.0774017 .0660201 -1.17 0.241 -.2069357 .0521324

_cons 10.99175 1.55593 7.06 0.000 7.938952 14.04454







Predictive margins Number of obs = 1148
Model VCE : OLS

Expression : Linear prediction, predict()


Delta-method
Margin Std. Err. t P>t [95% Conf. Interval]

female
0 14.62316 .4349116 33.62 0.000 13.76984 15.47647
1 13.3511 .4598713 29.03 0.000 12.44882 14.25339



. margins, at(age=(20(10)60))

Predictive margins Number of obs = 1148
Model VCE : OLS

Expression : Linear prediction, predict()

1._at : age = 20

2._at : age = 30

3._at : age = 40

4._at : age = 50

5._at : age = 60


Delta-method
Margin Std. Err. t P>t [95% Conf. Interval]

_at
1 13.1427 .4792111 27.43 0.000 12.20247 14.08293
2 13.95514 .3172715 43.98 0.000 13.33264 14.57764
3 14.76759 .4378812 33.73 0.000 13.90845 15.62673
4 15.58003 .70914 21.97 0.000 14.18867 16.97139
5 16.39247 1.016897 16.12 0.000 14.39728 18.38767


margins female, at(age=(20(10)60))

Predictive margins Number of obs = 1148
Model VCE : OLS

Expression : Linear prediction, predict()

1._at : age = 20

2._at : age = 30

3._at : age = 40

4._at : age = 50

5._at : age = 60


Delta-method
Margin Std. Err. t P>t [95% Conf. Interval]

_at#female
1 0 13.3475 .6876772 19.41 0.000 11.99825 14.69675
1 1 12.91372 .662621 19.49 0.000 11.61363 14.21381
2 0 14.52538 .4378656 33.17 0.000 13.66627 15.38449
2 1 13.31758 .4603422 28.93 0.000 12.41437 14.22079
3 0 15.70325 .6102808 25.73 0.000 14.50586 16.90065
3 1 13.72144 .6281752 21.84 0.000 12.48893 14.95394
4 0 16.88113 1.007496 16.76 0.000 14.90438 18.85788
4 1 14.1253 .9935462 14.22 0.000 12.17592 16.07467
5 0 18.059 1.455866 12.40 0.000 15.20254 20.91547
5 1 14.52916 1.410498 10.30 0.000 11.7617 17.29661



. margins, dydx(female) at(age=(20(10)60))

Conditional marginal effects Number of obs = 1148
Model VCE : OLS

Expression : Linear prediction, predict()
dy/dx w.r.t. : 1.female

1._at : age = 20

2._at : age = 30

3._at : age = 40

4._at : age = 50

5._at : age = 60


Delta-method
dy/dx Std. Err. t P>t [95% Conf. Interval]

1.female
_at
1 -.4337829 .9549693 -0.45 0.650 -2.307471 1.439905
2 -1.2078 .6353276 -1.90 0.058 -2.454338 .0387385
3 -1.981816 .875812 -2.26 0.024 -3.700194 -.2634381
4 -2.755833 1.414985 -1.95 0.052 -5.53209 .0204244
5 -3.52985 2.027079 -1.74 0.082 -7.50706 .4473607

Note: dy/dx for factor levels is the discrete change from the base level.



is the effect of age on seius different for male and female?

[Clyde Schechter]

is the effect of age on seius different for male and female

The answer to this question is found in the regression output, as the coefficient of 1.female#c.age. Specifically, the difference between the effect of age on seius in females is .0774017 lower than in males. Do also attend to the uncertainty in that estimate as reflected in the standard error and 95% confidence limits. In general, I do not pay much, if any, attention to statistical significance for interactions, but if you want to do that, you will note that the p-value here is 0.241.

The various marginal effects and predictive margins you have calculated are all interesting in their own right, but none of them answers the question you posed.

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