interactions and reference catagory in Margins

Paul Cauley

Join Date: Jan 2015

Posts: 7
#1

interactions and reference catagory in Margins

21 Jan 2015, 08:31

I have a question about interactions and the reference categories when using the margins command. Specifically, I want to compare all categories to the same base reference category. So, for example, I might have an interaction of dummy variables, age and gender like this:

reg income age##female
margins, over(r.age) at(female=(0 1))

This will give me the difference between age categories for males, and the difference between age categories for females.

But what I want to do is compare all groups to young males. Specifically, how can I get a "diagonal" difference that compares young males to older females?

Thanks in advance for advice.
Tags: None

Jeff Pitblado (StataCorp)

StataCorp Employee

Join Date: Mar 2014
Posts: 686

21 Jan 2015, 12:34

For contrasts of linear predictions, you can just specify the contrasts you want directly in marginlist.
You do not need to use over() or at().

Code:

margins r.age#r.female

In fact, you do not need margins, you can just use contrast directly.

Code:

contrast r.age#r.female

Here is an example using a dataset from the margins documentation.

Code:

. webuse margex 
(Artificial data for margins)

. regress y sex##group

      Source |       SS       df       MS              Number of obs =    3000
-------------+------------------------------           F(  5,  2994) =   92.91
       Model |  186898.199     5  37379.6398           Prob > F      =  0.0000
    Residual |  1204534.81  2994  402.316235           R-squared     =  0.1343
-------------+------------------------------           Adj R-squared =  0.1329
       Total |  1391433.01  2999  463.965657           Root MSE      =  20.058

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |
     female  |   21.62507   1.509999    14.32   0.000     18.66433    24.58581
             |
       group |
          2  |   11.37444   1.573314     7.23   0.000     8.289552    14.45932
          3  |    21.6188   1.588487    13.61   0.000     18.50416    24.73344
             |
   sex#group |
   female#2  |  -4.851582   1.942744    -2.50   0.013     -8.66083   -1.042333
   female#3  |  -6.084875   3.004638    -2.03   0.043    -11.97624   -.1935115
             |
       _cons |    50.6107   1.367932    37.00   0.000     47.92852    53.29288
------------------------------------------------------------------------------

. margins r.sex#r.group

Contrasts of adjusted predictions
Model VCE    : OLS

Expression   : Linear prediction, predict()

--------------------------------------------------------------
                           |         df           F        P>F
---------------------------+----------------------------------
                 sex#group |
(female vs male) (2 vs 1)  |          1        6.24     0.0126
(female vs male) (3 vs 1)  |          1        4.10     0.0429
                    Joint  |          2        3.77     0.0232
                           |
               Denominator |       2994
--------------------------------------------------------------

----------------------------------------------------------------------------
                           |            Delta-method
                           |   Contrast   Std. Err.     [95% Conf. Interval]
---------------------------+------------------------------------------------
                 sex#group |
(female vs male) (2 vs 1)  |  -4.851582   1.942744      -8.66083   -1.042333
(female vs male) (3 vs 1)  |  -6.084875   3.004638     -11.97624   -.1935115
----------------------------------------------------------------------------

. contrast r.sex#r.group

Contrasts of marginal linear predictions

Margins      : asbalanced

--------------------------------------------------------------
                           |         df           F        P>F
---------------------------+----------------------------------
                 sex#group |
(female vs male) (2 vs 1)  |          1        6.24     0.0126
(female vs male) (3 vs 1)  |          1        4.10     0.0429
                    Joint  |          2        3.77     0.0232
                           |
               Denominator |       2994
--------------------------------------------------------------

----------------------------------------------------------------------------
                           |   Contrast   Std. Err.     [95% Conf. Interval]
---------------------------+------------------------------------------------
                 sex#group |
(female vs male) (2 vs 1)  |  -4.851582   1.942744      -8.66083   -1.042333
(female vs male) (3 vs 1)  |  -6.084875   3.004638     -11.97624   -.1935115
----------------------------------------------------------------------------

Comment

Paul Cauley

Join Date: Jan 2015

Posts: 7
#3

28 Jan 2015, 13:53

Thanks - but I that syntax just gives me a second difference - it compares the difference between female/male in group one, to female/male in group 2.

I need to compare male in group 1, to female in group 2. That is, compare all combinations to the same base reference category (male/group 1)

Looking at the documentation, I think I have to use user-defined contrasts. Although I haven't been able to figure them out yet.

Paul
Comment
Clyde Schechter

Join Date: Apr 2014

Posts: 29958
#4

28 Jan 2015, 14:17

Well, one fairly simple approach would be to -egen group_gender = group(sex group)- and then use group_gender in place of group, sex, and their interaction in the regression. (To make it as simple as possible, set male in group 1 as the base category for group_gender.) Then run -margins group_gender-.
Comment

Jeff Pitblado (StataCorp)

StataCorp Employee

Join Date: Mar 2014
Posts: 686

29 Jan 2015, 08:02

As Paul indicated, this is possible with contrast with a custom contrast. In my example there
are 2 levels in sex (0 for male, 1 for female) and 3 levels in group (numbered 1 2 3).
We want the difference between the margins for 0.sex#1.group and 1.sex#2.group.

The interaction is organized as follows

Code:

i  sex  group
-----------------
1    0      1
2    0      2
3    0      3
4    1      1
5    1      2
6    1      3

The i above is an index, or position, that identifies which two margins Paul is interested in. Namely
1 for 0.sex#1.group and 5 for 1.sex#2.group. This tells us which position to put non-zero
values in our custom contrast. contrast allows us to leave off all trailing zeroes.

Code:

. contrast {sex#group 1 0 0  0 -1}

Contrasts of marginal linear predictions

Margins      : asbalanced

------------------------------------------------
             |         df           F        P>F
-------------+----------------------------------
   sex#group |          1      286.93     0.0000
             |
 Denominator |       2994
------------------------------------------------

--------------------------------------------------------------
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
   sex#group |
    (1) (1)  |  -28.14793   1.661722     -31.40616    -24.8897
--------------------------------------------------------------

As I just illustrated, contrast allows custom contrasts, but they can be difficult to develop and
the labeling can be quite cryptic.

An easier alternative for this case is pwcompare, which will produce a table of all
pairwise comparisons of the specified marginal linear predictions.

In the following, I believe Paul is interested in the row titled (female#2) vs (male#1).

Code:

. pwcompare sex#group

Pairwise comparisons of marginal linear predictions

Margins      : asbalanced

---------------------------------------------------------------------------
                          |                                 Unadjusted
                          |   Contrast   Std. Err.     [95% Conf. Interval]
--------------------------+------------------------------------------------
                sex#group |
    (male#2) vs (male#1)  |   11.37444   1.573314      8.289552    14.45932
    (male#3) vs (male#1)  |    21.6188   1.588487      18.50416    24.73344
  (female#1) vs (male#1)  |   21.62507   1.509999      18.66433    24.58581
  (female#2) vs (male#1)  |   28.14793   1.661722       24.8897    31.40616
  (female#3) vs (male#1)  |     37.159   2.822577      31.62461    42.69339
    (male#3) vs (male#2)  |   10.24436   1.120772        8.0468    12.44192
  (female#1) vs (male#2)  |   10.25064   1.006447      8.277239    12.22404
  (female#2) vs (male#2)  |   16.77349   1.222358      14.37675    19.17024
  (female#3) vs (male#2)  |   25.78456   2.588393      20.70935    30.85977
  (female#1) vs (male#3)  |   .0062748   1.030005     -2.013314    2.025864
  (female#2) vs (male#3)  |   6.529131   1.241826      4.094212     8.96405
  (female#3) vs (male#3)  |    15.5402   2.597644      10.44685    20.63355
(female#2) vs (female#1)  |   6.522856    1.13971      4.288163    8.757549
(female#3) vs (female#1)  |   15.53392   2.550404       10.5332    20.53465
(female#3) vs (female#2)  |   9.011069   2.643063      3.828666    14.19347
---------------------------------------------------------------------------

We can cut down on the volume of output by specifying levels for the factor variables.

Code:

. pwcompare i(0 1).sex#i(1 2).group

Pairwise comparisons of marginal linear predictions

Margins      : asbalanced

---------------------------------------------------------------------------
                          |                                 Unadjusted
                          |   Contrast   Std. Err.     [95% Conf. Interval]
--------------------------+------------------------------------------------
                sex#group |
    (male#2) vs (male#1)  |   11.37444   1.573314      8.289552    14.45932
  (female#1) vs (male#1)  |   21.62507   1.509999      18.66433    24.58581
  (female#2) vs (male#1)  |   28.14793   1.661722       24.8897    31.40616
  (female#1) vs (male#2)  |   10.25064   1.006447      8.277239    12.22404
  (female#2) vs (male#2)  |   16.77349   1.222358      14.37675    19.17024
(female#2) vs (female#1)  |   6.522856    1.13971      4.288163    8.757549
---------------------------------------------------------------------------

Comment

Paul Cauley

Join Date: Jan 2015

Posts: 7
#6

19 Jun 2015, 10:59

For future readers, pwcompare is exactly what I needed, and much easier to use than contrast. Many thanks to Jeff Pitblado.
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