Predictive margins for interactions

Mohieddine Rahmouni

Join Date: Aug 2020

Posts: 21
#1

Predictive margins for interactions

04 Mar 2023, 03:11

Dear stata Community,
The question is about the difference between the results of the following methods for determining the predictive margins of interactions between two variables:

webuse nhanes2f, clear

1) logit diabetes i.black i.female i.black#i.female, nolog
margin i.black#i.female

2) logit diabetes i.black i.female, nolog
margin i.black#i.female

Thank you in advance!
MR
Tags: None

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17854

04 Mar 2023, 03:40

Mohieddine:
your codes differ.
The first one is equivalent to:

Code:

logit diabetes  i.black##i.female, nolog

and both give back, as expected, the very same -margins- results:

Code:

. webuse nhanes2f, clear
. logit diabetes i.black i.female i.black#i.female, nolog

Logistic regression                                     Number of obs = 10,335
                                                        LR chi2(3)    =  25.18
                                                        Prob > chi2   = 0.0000
Log likelihood = -1986.4776                             Pseudo R2     = 0.0063

-------------------------------------------------------------------------------
     diabetes | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
        black |
       Black  |   .6645927   .1852115     3.59   0.000     .3015849    1.027601
              |
       female |
      Female  |   .1827775    .101556     1.80   0.072    -.0162685    .3818235
              |
 black#female |
Black#Female  |  -.1014563   .2479637    -0.41   0.682    -.5874561    .3845435
              |
        _cons |  -3.162571   .0763086   -41.44   0.000    -3.312134   -3.013009
-------------------------------------------------------------------------------

. margin i.black#i.female

Adjusted predictions                                    Number of obs = 10,335
Model VCE: OIM

Expression: Pr(diabetes), predict()

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   std. err.      z    P>|z|     [95% conf. interval]
------------------+----------------------------------------------------------------
     black#female |
  Not Black#Male  |   .0405988   .0029723    13.66   0.000     .0347733    .0464243
Not Black#Female  |   .0483471   .0030832    15.68   0.000     .0423041    .0543901
      Black#Male  |       .076   .0118511     6.41   0.000     .0527723    .0992277
    Black#Female  |   .0819113   .0113283     7.23   0.000     .0597082    .1041144
-----------------------------------------------------------------------------------

. . logit diabetes i.black##i.female, nolog

Logistic regression                                     Number of obs = 10,335
                                                        LR chi2(3)    =  25.18
                                                        Prob > chi2   = 0.0000
Log likelihood = -1986.4776                             Pseudo R2     = 0.0063

-------------------------------------------------------------------------------
     diabetes | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
        black |
       Black  |   .6645927   .1852115     3.59   0.000     .3015849    1.027601
              |
       female |
      Female  |   .1827775    .101556     1.80   0.072    -.0162685    .3818235
              |
 black#female |
Black#Female  |  -.1014563   .2479637    -0.41   0.682    -.5874561    .3845435
              |
        _cons |  -3.162571   .0763086   -41.44   0.000    -3.312134   -3.013009
-------------------------------------------------------------------------------

. margin i.black#i.female

Adjusted predictions                                    Number of obs = 10,335
Model VCE: OIM

Expression: Pr(diabetes), predict()

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   std. err.      z    P>|z|     [95% conf. interval]
------------------+----------------------------------------------------------------
     black#female |
  Not Black#Male  |   .0405988   .0029723    13.66   0.000     .0347733    .0464243
Not Black#Female  |   .0483471   .0030832    15.68   0.000     .0423041    .0543901
      Black#Male  |       .076   .0118511     6.41   0.000     .0527723    .0992277
    Black#Female  |   .0819113   .0113283     7.23   0.000     .0597082    .1041144
-----------------------------------------------------------------------------------

.

Kind regards,
Carlo
(Stata 19.0)

Comment

Mohieddine Rahmouni

Join Date: Aug 2020
Posts: 21

04 Mar 2023, 04:01

Thank you Carlo!

They do not give the same predictive margin, the second gives:

HTML Code:

. webuse nhanes2f, clear

quietly logit diabetes i.black i.female, nolog
margin i.black#i.female

Adjusted predictions                                    Number of obs = 10,335
Model VCE: OIM

Expression: Pr(diabetes), predict()

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   std. err.      z    P>|z|     [95% conf. interval]
------------------+----------------------------------------------------------------
     black#female |
  Not Black#Male  |   .0409717   .0028428    14.41   0.000     .0353998    .0465435
Not Black#Female  |   .0480074   .0029587    16.23   0.000     .0422085    .0538063
      Black#Male  |   .0727119   .0083843     8.67   0.000     .0562791    .0891448
    Black#Female  |   .0847168   .0092371     9.17   0.000     .0666124    .1028211
-----------------------------------------------------------------------------------

Comment

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17854

04 Mar 2023, 04:14

Mohieddine:
sorry for the possible confusion.
I meant that:

Code:

. . logit diabetes i.black i.female i.black#i.female, nolog

Logistic regression                                     Number of obs = 10,335
                                                        LR chi2(3)    =  25.18
                                                        Prob > chi2   = 0.0000
Log likelihood = -1986.4776                             Pseudo R2     = 0.0063

-------------------------------------------------------------------------------
     diabetes | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
        black |
       Black  |   .6645927   .1852115     3.59   0.000     .3015849    1.027601
              |
       female |
      Female  |   .1827775    .101556     1.80   0.072    -.0162685    .3818235
              |
 black#female |
Black#Female  |  -.1014563   .2479637    -0.41   0.682    -.5874561    .3845435
              |
        _cons |  -3.162571   .0763086   -41.44   0.000    -3.312134   -3.013009
-------------------------------------------------------------------------------

. . margin i.black#i.female

Adjusted predictions                                    Number of obs = 10,335
Model VCE: OIM

Expression: Pr(diabetes), predict()

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   std. err.      z    P>|z|     [95% conf. interval]
------------------+----------------------------------------------------------------
     black#female |
  Not Black#Male  |   .0405988   .0029723    13.66   0.000     .0347733    .0464243
Not Black#Female  |   .0483471   .0030832    15.68   0.000     .0423041    .0543901
      Black#Male  |       .076   .0118511     6.41   0.000     .0527723    .0992277
    Black#Female  |   .0819113   .0113283     7.23   0.000     .0597082    .1041144
-----------------------------------------------------------------------------------

is equivalent to:

Code:

. logit diabetes i.black##i.female, nolog

Logistic regression                                     Number of obs = 10,335
                                                        LR chi2(3)    =  25.18
                                                        Prob > chi2   = 0.0000
Log likelihood = -1986.4776                             Pseudo R2     = 0.0063

-------------------------------------------------------------------------------
     diabetes | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
        black |
       Black  |   .6645927   .1852115     3.59   0.000     .3015849    1.027601
              |
       female |
      Female  |   .1827775    .101556     1.80   0.072    -.0162685    .3818235
              |
 black#female |
Black#Female  |  -.1014563   .2479637    -0.41   0.682    -.5874561    .3845435
              |
        _cons |  -3.162571   .0763086   -41.44   0.000    -3.312134   -3.013009
-------------------------------------------------------------------------------

. . margin i.black#i.female

Adjusted predictions                                    Number of obs = 10,335
Model VCE: OIM

Expression: Pr(diabetes), predict()

-----------------------------------------------------------------------------------
                  |            Delta-method
                  |     Margin   std. err.      z    P>|z|     [95% conf. interval]
------------------+----------------------------------------------------------------
     black#female |
  Not Black#Male  |   .0405988   .0029723    13.66   0.000     .0347733    .0464243
Not Black#Female  |   .0483471   .0030832    15.68   0.000     .0423041    .0543901
      Black#Male  |       .076   .0118511     6.41   0.000     .0527723    .0992277
    Black#Female  |   .0819113   .0113283     7.23   0.000     .0597082    .1041144
-----------------------------------------------------------------------------------

.

Your codes cannot give back the same -margins- results, as, while your first code includes interactio and conditional main effects of the predictors included in the regression, the second code includes their intearctions only (an approach that is seldom used in empirical research).
Therefore, notwithstanding you asked -margins- to investigate -margin i.black#i.female- after each regression, as -margins- is basically fed by the regression specification, no wonder that you obtained different results.
For (much) more on this tois, I'd point you out to the -margins- entry, Stata .pdf manual.

Last edited by Carlo Lazzaro; 04 Mar 2023, 04:16.

Kind regards,
Carlo
(Stata 19.0)

Comment

Mohieddine Rahmouni

Join Date: Aug 2020

Posts: 21
#5

08 Mar 2023, 04:06

Thank you Carlo!
Comment

Announcement