Categorical interaction terms

[Ann Sannes]

Hi,
I am a bit lost in terms of how to interpret interaction effects between categorical variables.

We wanted to look at effects of time and genotype on pain over time. There are 3 time points and 3 genetic variants.

The code I used in my model is as such:
xtmixed pain time##genotype || ID:

the interaction term that results look like this:
time#genotype
2 2 | -.040
2 3 | .566
3 2 | -1.25
3 3 | .06

My question is: what is the reference here? Is it genotype 1 at baseline / genotype 1 at baseline compared to baseline value of genetic variant 2/3 / or something else?
Some help with this is highly appreciated!

Thanks in advance
Ann

[Andrew Musau]

Use margins to help with the interpretation. The reference categories are those that are omitted - and the coefficients on the interaction terms reflect differences in the effects of the interacting variable on the outcome between the subgroups. Reference categories in blue below:

webuse productivity, clear
set seed 05032023
gen zero1= runiformint(0,1)
mixed gsp private emp region##zero1 || state:, nolog
margins region##zero1, post
di (_b[2.region#1.zero1]- _b[1.region#1.zero1]) - (_b[2.region#0.zero1]- _b[1.region#0.zero1])

Res.:

. mixed gsp private emp region##zero1 || state:, nolog

Mixed-effects ML regression                     Number of obs     =        816
Group variable: state                           Number of groups  =         48

                                                Obs per group:
                                                              min =         17
                                                              avg =       17.0
                                                              max =         17

                                                Wald chi2(19)     =   19385.99
Log likelihood =   1388.234                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         gsp | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
     private |   .2296795   .0187202    12.27   0.000     .1929885    .2663704
         emp |   .8029527   .0207391    38.72   0.000     .7623049    .8436005
             |
      region |
          2  |   .0543114   .0594841     0.91   0.361    -.0622752     .170898
          3  |   .0008312   .0508529     0.02   0.987    -.0988387     .100501
          4  |  -.0014129   .0463764    -0.03   0.976     -.092309    .0894832
          5  |  -.0406748   .0441636    -0.92   0.357    -.1272339    .0458843
          6  |   -.068843   .0528847    -1.30   0.193    -.1724952    .0348091
          7  |   .0905332   .0549163     1.65   0.099    -.0171007    .1981671
          8  |   .0868273   .0458875     1.89   0.058    -.0031106    .1767652
          9  |   .0788121   .0583256     1.35   0.177     -.035504    .1931282
             |
     1.zero1 |   .0020372   .0078161     0.26   0.794     -.013282    .0173564
             |
region#zero1 |
        2 1  |  -.0143782   .0135599    -1.06   0.289     -.040955    .0121987
        3 1  |  -.0033918   .0117368    -0.29   0.773    -.0263955    .0196119
        4 1  |   .0068828   .0107094     0.64   0.520    -.0141072    .0278728
        5 1  |    .006554   .0103847     0.63   0.528    -.0137997    .0269077
        6 1  |  -.0007459   .0124319    -0.06   0.952     -.025112    .0236202
        7 1  |  -.0010905   .0124834    -0.09   0.930    -.0255574    .0233764
        8 1  |  -.0055484   .0103322    -0.54   0.591     -.025799    .0147023
        9 1  |  -.0006522   .0135303    -0.05   0.962     -.027171    .0258666
             |
       _cons |   2.461668   .0846728    29.07   0.000     2.295712    2.627624
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
state: Identity              |
                  var(_cons) |   .0062466   .0013323      .0041123    .0094885
-----------------------------+------------------------------------------------
               var(Residual) |   .0015168   .0000776      .0013721    .0016767
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 977.15        Prob >= chibar2 = 0.0000

. 
. margins region##zero1, post

Predictive margins                                         Number of obs = 816

Expression: Linear prediction, fixed portion, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
      region |
          1  |   10.49141   .0339533   308.99   0.000     10.42486    10.55796
          2  |   10.53834   .0480589   219.28   0.000     10.44414    10.63253
          3  |    10.4905   .0367019   285.83   0.000     10.41856    10.56243
          4  |   10.49353   .0305836   343.11   0.000     10.43359    10.55347
          5  |    10.4541   .0283585   368.64   0.000     10.39852    10.50968
          6  |   10.42218   .0398055   261.83   0.000     10.34417     10.5002
          7  |   10.58138   .0406848   260.08   0.000     10.50164    10.66112
          8  |   10.57539   .0299899   352.63   0.000     10.51661    10.63417
          9  |   10.56989   .0464166   227.72   0.000     10.47891    10.66086
             |
       zero1 |
          0  |   10.50806   .0115784   907.56   0.000     10.48537    10.53076
          1  |   10.50983   .0115694   908.42   0.000     10.48715     10.5325
             |
region#zero1 |
        1 0  |   10.49036   .0341951   306.78   0.000     10.42334    10.55738
        1 1  |    10.4924   .0341605   307.15   0.000     10.42545    10.55935
        2 0  |   10.54467   .0484924   217.45   0.000     10.44963    10.63972
        2 1  |   10.53233   .0482675   218.21   0.000     10.43773    10.62694
        3 0  |   10.49119   .0369675   283.80   0.000     10.41874    10.56365
        3 1  |   10.48984   .0369566   283.84   0.000     10.41741    10.56227
        4 0  |   10.48895   .0308038   340.51   0.000     10.42858    10.54932
        4 1  |   10.49787   .0307995   340.84   0.000      10.4375    10.55824
        5 0  |   10.44969   .0285474   366.05   0.000     10.39374    10.50564
        5 1  |   10.45828   .0285791   365.94   0.000     10.40227    10.51429
        6 0  |   10.42152   .0401361   259.65   0.000     10.34285    10.50019
        6 1  |   10.42281   .0400614   260.17   0.000     10.34429    10.50133
        7 0  |    10.5809   .0410393   257.82   0.000     10.50046    10.66133
        7 1  |   10.58184   .0409132   258.64   0.000     10.50165    10.66203
        8 0  |   10.57719   .0302127   350.09   0.000     10.51797    10.63641
        8 1  |   10.57368   .0301478   350.73   0.000     10.51459    10.63277
        9 0  |   10.56918   .0468261   225.71   0.000      10.4774    10.66095
        9 1  |   10.57056   .0466655   226.52   0.000      10.4791    10.66202
------------------------------------------------------------------------------

. 
. di (_b[2.region#1.zero1]- _b[1.region#1.zero1]) - (_b[2.region#0.zero1]- _b[1.region#0.zero1])
-.01437815

.

[Maarten Buis]

You can add the baselevel option to xtmixed to show you what the references are.

My guess would be time=1 and genotype=1, but without your data that is only a guess.