I want to test whether an intervention affects a continuous outcome over 5 possible time points. How do I decide whether to include random slopes? I want slope to be able to vary between intervention group (by including a time * intervention interaction fixed effect) but not necessarily person to person within treatment group. From a theoretical standpoint, I would expect different people in the population to have different slopes for this outcome (anxiety) simply since there are so many factors that impact it, but I mostly care about the effect of the intervention. Intervention group was randomized. Is there a clear theory-based reason to go either way? Should I be using the (SPSS output) value of variance of the slope to help make that decision (farther from zero = random slopes more important)? I included a covariance significance test (TESTCOV in PRINT subcommand) in my output as well, and the random slopes are statistically significant in the Estimates of Covariance Parameters table, but I also read that many statisticians don't agree with the use of that test.
There are two main considerations when choosing whether to specify random slopes for a variable:
Is it biologically / clinically / theoretically possible for each subject (or whatever the grouping variable is) to have their own slope with respect to that variable ? Obviously this also implies that the variable varies within level of the grouping variable.
Does the data support a model with random slopes ? That is, does the model converge normally ? Quite often the inclusion of random slopes leads to convergence problems, especially when correlations between the intercepts and slopes are also estimated.
I would refrain from any significance tests. If random slopes are justified and the model converges, retain the random slopes.