margins, dydx() question

[Lucy Hiscox]

Hi,

Just a quick question.

Just say you were to find a significant interaction between two categorical variables (each with 2 levels).

Say one of those variables was sex, which had acted as a moderator on the main variable of interest.

How would you report the use of margins sex, dydx(X) in the results?

I am surprised that this command does not produce the same results as a sex-stratified model?

Thanks for you advice.

Lucy

[Felix Bittmann]

The command you post gives you the marginal effect of X on the outcome, which might be different for the two sexes. For example, the effect X has on Y for male is -1, but for women it is +1. This is a quite interesting finding as it shows you hat Xs works differently for the sexes.

Regarding the second question, I assume that control variables make a difference. In a sex-stratified model (so two regressions for each subsample), there is an implicit interaction included between sex and each other control by design. To get the same results in a single model you need something like

reg y i.x##i.sex i.sex##(c.control1 c.control2)

[Lucy Hiscox]

That's really helpful, thank you.

Would it be correct then to do:
reg y i.x##i.sex c.control1 c.control2 margins sex, dydx(X)

and say these results are "stratified by sex"? (i.e. I am not sure how to report these results in a paper)

These results provide a significant p value for females, but not for males. But in the 2 separate sex stratified models, the impact of X is not significant for either sex.

Does the margins command consider the impact of the control variables?

[Lucy Hiscox]

p.s. that code was meant to be over two separate lines!

[Felix Bittmann]

The command you show in post 3 is not fully stratified since there is no interaction for control1 and control2. To be explicit, you need

reg y i.x##i.sex i.sex##c.control1 i.sex##c.control2

To give a concrete example:

. sysuse auto, clear
(1978 Automobile Data)

. bysort foreign: reg mpg weight price headroom

------------------------------------------------------------------------------------------------------------------
-> foreign = Domestic

      Source |       SS           df       MS      Number of obs   =        52
-------------+----------------------------------   F(3, 48)        =     59.75
       Model |  905.081523         3  301.693841   Prob > F        =    0.0000
    Residual |  242.360785        48  5.04918302   R-squared       =    0.7888
-------------+----------------------------------   Adj R-squared   =    0.7756
       Total |  1147.44231        51  22.4988688   Root MSE        =     2.247

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0062287   .0006945    -8.97   0.000    -.0076252   -.0048322
       price |    .000191   .0001412     1.35   0.182    -.0000929    .0004749
    headroom |  -.5451166   .3943986    -1.38   0.173    -1.338108     .247875
       _cons |   41.04741    1.65969    24.73   0.000     37.71038    44.38444
------------------------------------------------------------------------------

------------------------------------------------------------------------------------------------------------------
-> foreign = Foreign

      Source |       SS           df       MS      Number of obs   =        22
-------------+----------------------------------   F(3, 18)        =      5.57
       Model |  441.736499         3    147.2455   Prob > F        =    0.0070
    Residual |  476.127137        18  26.4515076   R-squared       =    0.4813
-------------+----------------------------------   Adj R-squared   =    0.3948
       Total |  917.863636        21  43.7077922   Root MSE        =    5.1431

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0087963   .0055794    -1.58   0.132    -.0205181    .0029255
       price |  -.0003344   .0009221    -0.36   0.721    -.0022717    .0016029
    headroom |   1.478554   2.321062     0.64   0.532    -3.397816    6.354925
       _cons |   43.41484   10.02813     4.33   0.000     22.34653    64.48316
------------------------------------------------------------------------------

. reg mpg c.weight##i.foreign i.foreign##(c.price c.headroom)

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(7, 66)        =     22.64
       Model |  1724.97154         7  246.424505   Prob > F        =    0.0000
    Residual |  718.487922        66  10.8861806   R-squared       =    0.7060
-------------+----------------------------------   Adj R-squared   =    0.6748
       Total |  2443.45946        73  33.4720474   Root MSE        =    3.2994

------------------------------------------------------------------------------------
               mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
            weight |  -.0062287   .0010198    -6.11   0.000    -.0082648   -.0041926
                   |
           foreign |
          Foreign  |   2.367435   6.879391     0.34   0.732    -11.36771    16.10258
                   |
  foreign#c.weight |
          Foreign  |  -.0025676   .0037217    -0.69   0.493    -.0099983    .0048631
                   |
             price |    .000191   .0002073     0.92   0.360    -.0002229     .000605
          headroom |  -.5451166   .5791121    -0.94   0.350    -1.701351     .611118
                   |
   foreign#c.price |
          Foreign  |  -.0005254   .0006268    -0.84   0.405    -.0017769    .0007261
                   |
foreign#c.headroom |
          Foreign  |   2.023671   1.597667     1.27   0.210    -1.166173    5.213515
                   |
             _cons |   41.04741   2.436992    16.84   0.000      36.1818    45.91302
------------------------------------------------------------------------------------

. margins, dydx(weight) by(foreign)

Average marginal effects                        Number of obs     =         74
Model VCE    : OLS

Expression   : Linear prediction, predict()
dy/dx w.r.t. : weight
over         : foreign

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight       |
     foreign |
   Domestic  |  -.0062287   .0010198    -6.11   0.000    -.0082648   -.0041926
    Foreign  |  -.0087963   .0035793    -2.46   0.017    -.0159426     -.00165
------------------------------------------------------------------------------

As you see, what margins gives you is exactly what the separate regressions produce for the coef of weight.


(The command I showed above with the parentheses is just a shortcut notation)

And yes, margin will adjust for all control variables in the model when computing the marginal effect. In a linear regression (regress) what margin does is rather straightforward and not even required, you could compute it manually from the regression and interaction coefficients. But ofc this is a bit tedious, especially in more complex models.

[Lucy Hiscox]

Thank you very much - I really appreciating you walking this through with me!

My follow up questions are:

1) In the initial stratified model for 'foreign', the regression p-value for weight is 0.132. I can see how the margins command produces the same coefficient (-0.0087963) but now the p value is statistically significant (0.000). Which p value should be reported?

2) Which model would be best to use to get adjusted means for each group?

For example, would it be:
reg mpg c.weight##i.foreign i.foreign##(c.price c.headroom)

margins foreign#weight

(of course would need to assume weight was a factor variable for this command to work)

or, the original model:
reg mpg c.weight##i.foreign c.price c.headroom margins

foreign#weight

3) Similarly, if you were to assume that both weight and foreign were factor variables, to look at posthoc simple effects would you use either:

reg mpg c.weight##i.foreign i.foreign##(c.price c.headroom)

contrast foreign@weight

or the original model:

reg mpg c.weight##i.foreign c.price c.headroom margins

contrast foreign@weight

(I assume the latter?)

Many thanks,
Lucy