Linear probability models with interactions: how can I calculate relative effects / relative risk ratios?

[Michael Richter]

Dear Statalisters,

I am running Linear Probability Models with interactions and would like to calculate relative effects.

Here is an example. I use the nlsw88-data and regress the probability of being married against an interaction between college attainment (binary) and income (continuous). What I want to calculate: the relative effect of college attainment, at different income levels, e.g. at values 5, 10 and 15.

Here is my code:

sysuse nlsw88,clear
reg married i.collgrad##c.wage
margins collgrad, at(wage== (5 10 15)) post

The margins-command gives me this result:

                        
. margins collgrad, at(wage== (5 10 15)) post

Adjusted predictions                            Number of obs     =      2,246
Model VCE    : OLS

Expression   : Linear prediction, predict()

1._at        : wage            =           5

2._at        : wage            =          10

3._at        : wage            =          15

-------------------------------------------------------------------------------------
                    |            Delta-method
                    |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
       _at#collgrad |
1#not college grad  |   .6452051   .0123095    52.42   0.000     .6210659    .6693443
    1#college grad  |   .6846007   .0275997    24.80   0.000      .630477    .7387244
2#not college grad  |   .6331711   .0134103    47.22   0.000     .6068732    .6594691
    2#college grad  |   .6502325    .020849    31.19   0.000     .6093471    .6911179
3#not college grad  |   .6211372   .0211735    29.34   0.000     .5796154    .6626589
    3#college grad  |   .6158643   .0254564    24.19   0.000     .5659437    .6657849
-------------------------------------------------------------------------------------

What I want now is calculate the relative effect of college education. This should be similar to the Relative Risk Ratio (RRR).
I could do this by hand: divide the predicted probability of being married for those with college attainment by the value for those without college attainment; separately for all levels of income. For the low income group, I would calculate: .6846007 / .6452051.
Here is how I could do this in Stata:

. display e(b)[1,2] / e(b)[1,1]
1.0610591

. display e(b)[1,4] / e(b)[1,3]
1.0269459

. display e(b)[1,6] / e(b)[1,5]
.99151097

But: this will not give me standard errors / confidence intervals.
How can I calculate these ratios including standard errors / confidence intervals?
In the third step, I would like to plot these ratios.


I'm using Stata 16.1.

Best
Michael