I am trying to analyze the data of a study in which I have compared the development of insulin resistance (IR) in 3 treatment group in a longitudinal setting (IR) measured every 3 weeks in all 3 group (a total of 12 weeks, so n=4 for the repeated measurement).
I have built a linear mixed model in which treatment is factor and time the covariate. Since, I am particularly interested in the time*treatment interaction I did put it also in my model, and I get a significant value.
My question: Which test should I run to see between which groups there is a sig time*treatment interaction. And is also possible to look per time point?
I am using SPSS.
Thanks in advance
As I see it from the information provided, you want to compare the slopes (time:Treatment) among the three treatment groups. You only have three pairwise comparisons, so it might be sufficient to simply predict the three slopes and the standard errors of their differences and then conduct t-test between these. As these are only three tests, I would use a simple Bonferroni correction (here: each P-value*3). I do not use SPSS, so I do not know how this would be performed. If you are lucky and you have balanced data and equal variances you could also use the Tukey procedure instead of t-tests to test for pairwise differences between the three slopes.
Testing for pairwise differences for each time point of your longitudinal design is the same as for slopes, you just do it for intercepts (or call it elevation as they are not at time = zero). Again, you just need to predict the Treatment means and the corresponding standard errors of the differences, but here for the intercepts at your selected time point.
Thanks, i will try it out.
To understand it cleary, i have to run the mixed model 3 times ( group 1 vs 2, 1 vs 3, and 2 vs 3) and mupltiple each time*treatment p value by 3 to correct for multiple comparison?
No, you just run the model once. The post-hoc pairwise tests for differences between the three treatment means are conducted on the predicted model means. You probably tested each term in the model (i.e., 'time', 'Treatment', 'time:Treatment') using F-tests or something similar and you found that the slopes differ among the three Treatment levels (= 'time:Treatment'). Now, you have to add a second step of analysis on the model results if you are interested in between which of the three levels of your model term differences are present. Unfortunately I don't know SPSS, so I cannot tell you how to do this using this programme. Maybe consult the SPSS manual to find out what your options for post-hoc tests are.
The correction of the three P-values would be, in its simplest case, like you described, but NOT for results on three models. Instead, you do it for the comparisons between the three model means from the same model (sometimes what I call here 'model means' are called 'least square means', or 'predicted means').
I assume that you are talking of a fixed effect model with time treated as covariate and treatment as factor. You can ask for the parameters, which give you a reference group contrast, reference group is the one which has no estimate.
You can specify user specified tests using the test - statement via syntax.
Another (may be the simplest) option is to omit the main effect of the covariate from the fixed effects model leaving only the treatment and the interaction. The parameter table (ineraction terms) then show the seperate slope estimates and their standard errors and confidence intervals. If your effects are clear it may be sufficient to just compere the confidence intervals. If not you can perform t-tests using these informations 'by hand'.
To do comparisons on time points you need to specify time as a factor. You can specify the tests by the test statement via syntax.
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