Contrasts after xtmixed

[Rena Jenkins]

Hi Stata forum members

I need help with "contrast" syntax. I have a continuous outcome measured at baseline and at three time points. There is an exposure variable (four-level) measured between the baseline and I am running the following random effects model:

xtmixed outcome i.exposure##time outcome_bl || id:

How can I test the contrast (-1, 0.5, 0.5) in time i.e. between time period 1 and the average of time periods two and three?

How can I then test the interaction of time--contrasting level 1 versus levels 2 and 3--and exposure?

Thank you

Rena

[Clyde Schechter]

Well, there are several ways to do this. But for this particular contrast, the simplest way would be to generate a new time variable that collapses the distinction between 2 and 3: -recode time (3=2), gen(time23)- and then run your model using ib2.time23 in place of time. This will set the referent category to a variable that indifferently denotes 2 and 3, and you will get an explicit effect for time = 1 and the interactions of that with exposure in the output.

This kind of trick, transforming the variables, is easy for this particular kind of contrast. For more general contrasts it can be very difficult to figure out what to do, and it won't be apparent when you come back months later just what you did or why. The more general approach is to use the -test- command for the hypothesis test, and the -lincom- command to estimate the contrast:

lincom 1.time - 0.5*2.time - 0.5*3.time
test 1.time = 0.5*2.time + 0.5*3.time

[Rena Jenkins]

Thanks again Clyde. Just out of curiosity: would it be possible to test for interactions between time--contrasting as above--and exposure using the lincom approach?

[Jeff Pitblado (StataCorp)]

In the following example I use regress but the concepts follow even
when used with mixed (or xtmixed in Stata 12).

First consider a simpler model without the interaction:

. webuse margex
(Artificial data for margins)

.
. regress y i.outcome i.group

      Source |       SS       df       MS              Number of obs =    3000
-------------+------------------------------           F(  3,  2996) =   11.45
       Model |   15778.351     3  5259.45035           Prob > F      =  0.0000
    Residual |  1375654.65  2996   459.16377           R-squared     =  0.0113
-------------+------------------------------           Adj R-squared =  0.0103
       Total |  1391433.01  2999  463.965657           Root MSE      =  21.428

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   1.outcome |   -2.02553   1.102687    -1.84   0.066    -4.187631    .1365713
             |
       group |
          2  |  -.0217244   .9211469    -0.02   0.981    -1.827869     1.78442
          3  |   4.782014   1.076471     4.44   0.000     2.671317     6.89271
             |
       _cons |   68.99662   .7097933    97.21   0.000     67.60489    70.38835
------------------------------------------------------------------------------

Clyde points out that we can use lincom to compute the contrast
of interest.

. lincom 1.group - (2.group + 3.group)/2

 ( 1)  1b.group - .5*2.group - .5*3.group = 0

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -2.380145   .8549784    -2.78   0.005    -4.056549   -.7037405
------------------------------------------------------------------------------

This can also be done with the Helmert contrast operator h..
In the following output, the contrast of interested is labelled
(1 vs >1).

. contrast h.group

Contrasts of marginal linear predictions

Margins      : asbalanced

------------------------------------------------
             |         df           F        P>F
-------------+----------------------------------
       group |
  (1 vs >1)  |          1        7.75     0.0054
  (2 vs  3)  |          1       21.16     0.0000
      Joint  |          2       12.61     0.0000
             |
 Denominator |       2996
------------------------------------------------

--------------------------------------------------------------
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
       group |
  (1 vs >1)  |  -2.380145   .8549784     -4.056549   -.7037405
  (2 vs  3)  |  -4.803738   1.044341     -6.851436    -2.75604
--------------------------------------------------------------

The reason I mention contrast is that it automatically accounts for
interactions, while lincom requires more of the user when models
contain interactions.

To illustraite, let's refit the model to also include the interaction.

. regress y outcome##group

      Source |       SS       df       MS              Number of obs =    3000
-------------+------------------------------           F(  5,  2994) =    9.24
       Model |  21137.6189     5  4227.52378           Prob > F      =  0.0000
    Residual |  1370295.39  2994   457.68049           R-squared     =  0.0152
-------------+------------------------------           Adj R-squared =  0.0135
       Total |  1391433.01  2999  463.965657           Root MSE      =  21.393

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   1.outcome |  -4.383724    1.32976    -3.30   0.001     -6.99106   -1.776388
             |
       group |
          2  |  -1.396504   1.006866    -1.39   0.166    -3.370722     .577715
          3  |    4.07282   1.115188     3.65   0.000     1.886208    6.259433
             |
     outcome#|
       group |
        1 2  |   8.495807   2.490864     3.41   0.001     3.611828    13.37978
        1 3  |     .89583   5.573102     0.16   0.872    -10.03167    11.82333
             |
       _cons |   69.74007   .7466372    93.41   0.000      68.2761    71.20405
------------------------------------------------------------------------------

If we use the same contrast with lincom we get

. lincom 1.group - (2.group + 3.group)/2

 ( 1)  1b.group - .5*2.group - .5*3.group = 0

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -1.338158    .918199    -1.46   0.145    -3.138523    .4622064
------------------------------------------------------------------------------

which does not account for the interaction between group and outcome.
But contrast will account for this in its calculations.

. contrast h.group

Contrasts of marginal linear predictions

Margins      : asbalanced

------------------------------------------------
             |         df           F        P>F
-------------+----------------------------------
       group |
  (1 vs >1)  |          1        5.33     0.0211
  (2 vs  3)  |          1        0.33     0.5654
      Joint  |          2        3.52     0.0297
             |
 Denominator |       2994
------------------------------------------------

--------------------------------------------------------------
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
       group |
  (1 vs >1)  |  -3.686068    1.59688      -6.81716    -.554975
  (2 vs  3)  |  -1.669336   2.903763     -7.362908    4.024236
--------------------------------------------------------------

We can also get contrast to produce contrasts of one factor variable
for each level of the other. Here we ask for Helmert contrasts of group
at each level of outcome.

. contrast h.group@outcome

Contrasts of marginal linear predictions

Margins      : asbalanced

-------------------------------------------------
              |         df           F        P>F
--------------+----------------------------------
group@outcome |
 (1 vs >1) 0  |          1        2.12     0.1451
 (1 vs >1) 1  |          1        3.89     0.0486
 (2 vs  3) 0  |          1       26.18     0.0000
 (2 vs  3) 1  |          1        0.14     0.7090
       Joint  |          4        9.25     0.0000
              |
  Denominator |       2994
-------------------------------------------------

---------------------------------------------------------------
              |   Contrast   Std. Err.     [95% Conf. Interval]
--------------+------------------------------------------------
group@outcome |
 (1 vs >1) 0  |  -1.338158    .918199     -3.138523    .4622064
 (1 vs >1) 1  |  -6.033977   3.058923     -12.03178    -.036173
 (2 vs  3) 0  |  -5.469324   1.068873     -7.565124   -3.373525
 (2 vs  3) 1  |   2.130653   5.708315     -9.061964    13.32327
---------------------------------------------------------------

This shows us that the lincom result is actually a partial effect of group
when outcome is 0.

[Rena Jenkins]

Sorry I have been away and missed this reply. Thanks Jeff, that's very helpful.