Need help to interpret the interaction term in longitudinal data

[Mengmeng Li]

Hi statisticians,

I am new to longitudinal data analysis, and currently learning by myself to be able to carry out hypothesis testing.

I have a short longitudinal data in terms of limited repeated measures (only baseline and time-1 post baseline are available). Also there is a group indicator ("studygroup") to suggest control versus intervention group. The goal of analysis is to evaluate if the trend of outcome (from baseline to time-1) differs between groups (control vs. intervention).

Variables:

• outcome: meanscore_sds (calculated based on a scale, ranging from 1-5)
• time variable: time (0: baseline; 1: time-1)
• group indicator: studygroup (0: control; 1: intervention)
• sex: (0: boy; 1: girl)
• id variable: surid

global restrict = "t1dropcase == 0 & t2dropcase == 0" // limit to eligible analytical sample 
mixed meanscore_sds time##studygroup if $restrict || surid: , residual(uns, t(time)) var ml

Results from above model:

                                                Wald chi2(3)      =      17.65
Log likelihood = -6160.3764                     Prob > chi2       =     0.0005

---------------------------------------------------------------------------------
  meanscore_sds |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
         2.time |   .0660626   .0308159     2.14   0.032     .0056645    .1264606
                |
     studygroup |
  Intervention  |   .0048707     .03559     0.14   0.891    -.0648845    .0746259
                |
time#studygroup |
2#Intervention  |   .0393069   .0432313     0.91   0.363     -.045425    .1240387
                |
          _cons |   4.276469   .0253691   168.57   0.000     4.226747    4.326191
---------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
surid: Identity              |
                  var(_cons) |   .0984436   1.990941      6.00e-19    1.61e+16
-----------------------------+------------------------------------------------
Residual: Unstructured       |
                     var(e1) |    .682875   1.991058      .0022516    207.1039
                     var(e2) |   .5772798   1.991008      .0006693     497.893
                  cov(e1,e2) |   .0536583   1.990978     -3.848587    3.955904
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 123.58                Prob > chi2 = 0.0000

My interpretations:

• coefficient for "time": among control group, outcome change at time1 compared to baseline
• coefficient for "studygroup": outcome in intervention compared to control control at baseline
• but I am not sure how to interpret the coefficient for interaction term. Is it the difference of baseline-time1 trend between two groups? Or is it the difference of outcome at time1 between intervention and control?

Thank you so much!!

Best,
Mengmeng

[Phil Bromiley]

You have 4 categories t & s=0, t&s=1, t=1 s=0, and t=0 s=1 and are essentially doing difference versus the first category. For some, the effect is the sum of parameters. Often, margins makes it easier to understand such results. The interaction is the change in the effect of study group when t=1 vs t=0 or vice versa.