Interpreting results from linear mixed effects model on repeated measures - interaction and main effects

[Rasmus Tougaard]

Dear all.
I'm fairly new to linear mixed effects models and so apologize in advance if my questions are very basic.
I need help understanding what my results mean, and hope you can provide it.

My data is derived from a design wherein I measured a parameter, "metabolism" on 36 subjects (identified by "id") in three groups (1, 2 and 3 in "group") at two different time points (1 and 2 in "time"). I am interested in:

1) Does metabolism in the three groups differ from each other at the time point 1 and time point 2?
2) Does metabolism change over time?
3) Does being in a certain group change how metabolism changes over time?

I am using Stata 14.2 and run the following command:

xtmixed metabolism group##time || id:, var

and get the following output:

. xtmixed metabolism group##time || id:, var

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0: log likelihood = 121.88734
Iteration 1: log likelihood = 122.32628
Iteration 2: log likelihood = 122.32652
Iteration 3: log likelihood = 122.32652

Computing standard errors:

Mixed-effects ML regression Number of obs = 67
Group variable: id Number of groups = 36

Obs per group:
min = 1
avg = 1.9
max = 2

Wald chi2(5) = 15.46
Log likelihood = 122.32652 Prob > chi2 = 0.0086

------------------------------------------------------------------------------
metabolism | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
group |
2 | -.0126059 .0162712 -0.77 0.438 -.0444968 .0192849
3 | .0139877 .0177918 0.79 0.432 -.0208836 .0488591
|
2.time | .0323302 .0159135 2.03 0.042 .0011403 .0635201
|
group#time |
2 2 | -.0126164 .0223585 -0.56 0.573 -.0564382 .0312054
3 2 | -.0028619 .0243949 -0.12 0.907 -.0506751 .0449513
|
_cons | .1481151 .0112525 13.16 0.000 .1260605 .1701697
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity |
var(_cons) | 3.38e-22 2.59e-21 1.02e-28 1.12e-15
-----------------------------+------------------------------------------------
var(Residual) | .0015194 .0002625 .001083 .0021318
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 0.00 Prob >= chibar2 = 1.0000

I then run

contrast group##time

and get the following:

. contrast group##time

Contrasts of marginal linear predictions

Margins : asbalanced

------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
metabolism |
group | 2 7.06 0.0293
|
time | 1 7.89 0.0050
|
group#time | 2 0.35 0.8415
------------------------------------------------

So, it seems there's a difference between groups, and that metabolism changes over time, but no interaction means that being in a certain group doesn't impact how metabolism changes over time. Am I correct here?

Now, to go further and answer my first question above, what can I do? I could run

contrast group@time, effect

which would look like this:

. contrast group@time, effect

Contrasts of marginal linear predictions

Margins : asbalanced

------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
metabolism |
group@time |
1 | 2 2.17 0.3387
2 | 2 5.61 0.0606
Joint | 4 7.77 0.1003
------------------------------------------------

--------------------------------------------------------------------------------
| Contrast Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
metabolism |
group@time |
(2 vs base) 1 | -.0126059 .0162712 -0.77 0.438 -.0444968 .0192849
(2 vs base) 2 | -.0252223 .0153346 -1.64 0.100 -.0552777 .004833
(3 vs base) 1 | .0139877 .0177918 0.79 0.432 -.0208836 .0488591
(3 vs base) 2 | .0111259 .0166902 0.67 0.505 -.0215863 .0438381
--------------------------------------------------------------------------------

Here we see whether there are any differences between the groups at the two time points and "joint", and it appears there are no differences between groups, which I am a little confused about, since the contrast group##time command told me there was a differences between groups. Can anyone help explaining this? And; am I even allowed to use the contrast group@time, effect command when no interaction is present? Or does the fact that no interaction is present mean I should simply run oneway anova, restricted to the two time points, as in these two commands:

oneway metabolism group if time==1, sidak tabulate
oneway metabolism group if time==2, sidak tabulate

Thank you so much in advance - I really appreciate any help you can give me in understanding these results.

Sincerely

Rasmus