Need help to choose a covariance structure for a repeated measures analysis in glimmix

[marcel]

I am analyzing a repeated measures experiment in glimmix. I have a treatment group and a control group.My main question is if the interaction between time*and treatment is significant. A simple ls-means table will suffice to me. I do not want to predict any measurements.

The Covariance as a Function of Lag in Time between Pairs of Observations looks like this:

I checked "Stroup et al. 2018. SAS for Mixed Models. Introduction and basic Applications" on this topic and I found out that it seems that AR(1) is a good simple structure for most cases. In fact, Stroup et al. read: "if non-negligible distance dependent within-subject correlation exists, switching from CS to AR(1) accomplishes the first 90% for accounting for within-subject correlation as a function of distance apart in time.

Given the above, I have two questions:

1) Is it better to always go with a "simpler" covariance structure, as long as the results are similar to those obtained when running models with more complex covariance structures?

2) are there considerations that may force me to go for a more "complicate" structure?

The evaluation of the different covariance structures for my model shows the following:

It seems that ARH(1) is better than AR(1). AR(1), as "simple" as it is, it has a large residual. Take a look at these two fit statistics for AR(1).

 
Generalized Chi-Square     4830671      
Gener. Chi-Square / DF     7958.27     

ARH(1) has better values for these two:

Generalized Chi-Square      618.88      
Gener. Chi-Square / DF      1.02     

However, the more complex ANTE(1) seems to be even better than the two above, judging by the AIC, AICC, BIC and log likelihood values below:

 Fit Statistics          
-2 Res Log Likelihood       6977.15      
AIC (smaller is better)       7021.15      
AICC (smaller is better)    7022.88      
BIC (smaller is better)       7046.13     
 
Generalized Chi-Square    619.29      
Gener. Chi-Square / DF    1.02     

Technically, ARH(1) and ANTE(1) are better than AR(1), and ANTE(1) is the best of all.

The model with AR(1) shows that the interaction Treat*Time is significant (this is my main question). This interaction is also significant with models with ARH(1) and ANTE(1).

Again, my question 1, reformulated here should read: Is it fine if I run my final model with an AR(1) covariance structure (simpler structure, but higher residual variability than ARH(1) and ANTE(1))?

Thank you in advance for your help.

Regards,

Marcel

[SteveDenham · Accepted solution]

Sorry I was late in answering @marcel , but see what I posted for Re: Clarification needed for glimmix covariance parameters test.  The answer is not to pick the simplest, but to pick the one that retains the most information (based on AIC or corrected AIC), so long as that structure is appropriate for the data generating process.

SteveDenham