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.
Random Slopes in a Growth Curve Analysis: Comprehensive Guide
growth-modelpanel datarandom-effects-modelspss
Related Solutions
You should ideally specify your unadjustet and adjusted model beforehand offcourse. A sound scientific practice requires that the variables for the adjusted model should be decided apriori on based on prior knowledge of variables that have a high correlation with the dependent (outcome variable) and variables should not be cherry-picked from analysing baselinedata. Also beware of the risk of overfitting by throwing too many variables into the model and playing fort and back with putting variables in and leaving them out (lot of litterature on this topic). Regarding your outcome variable however, baseline differences between groups shoul allways be adjusted for and specified in a traditional ANCOVA (e.g. linear regression) (see Altman / Vickers for traditional points on adjusting for dependent variable baseline in the BMJ series on statistic).
However, the topic of how to specify the model and adjust for baseline-differences of the dependent variable between groups is a hot one when it comes to mixed model. (see Twisk 2018 (some errors in this article) and se articles and a freshly published book on analysing randomized trials with mixed model by a japaneese statitistician: Toshiro Tango)
So far I am inclined to follow Tango's suggestions. Thus, specifying the model similar to like this (random intercept):
Yt (ij) = B0 + B1 X + B2 time + B3 time*group + b(ij) + e(ij)
Were Yt is the outcome/dependent variable (walking time in your case). "t" denotes that Y is a function of time (ij) denotes that Y is based on repeated meassurements nested in each individual(i) and time(j). B0 - denotes regression coefficient for the control group - i.e. mean at baseline B1 - denotes the baseline differnce for the treatment group (X specified as 0 for control group and 1 for treatment group) B2 - effect of time for the control group - i.e. post mean value is B0+B2 B3 - the difference in effect of time*group - i.e. the difference between control and treatment - this is the coefficient you normally would use to assess the effect estimate of the treatment compared to control and conclude on wheather to reject H0 (that the there is noe difference between groups). Bij is here the random intercept - basically just assessing the individual variance at baseline - it should by definition be a normal distribution with mean 0. eij is the error term (This model is simplified a bit by leaving out random slope which is a debate of it's own)
This model is only specified with time as pre post, but with repeated meassurements you just add time points and interaction between time and group - e.g. B4 time2 B6 time2*X B7 time 3 ... etc). If you only have baseline and one follow up meassurment then traditonal ACOVA (regression) might be a better choice than mixed model. One of the great advantages of mixed model is the way you can handle missing without imputation etc. as long as you can assume missing at random.
Since I do not use SPPS I cannot help you with the exact syntax for running th model above in SPSS, but I bet others can. Hope it was a bit helpfull even though this topic can be more confusing than one would expect at first.
Is there a reason that I would want to include Group x Time as a random effect, vs. only keeping it in the fixed effects portion of the model?
Yes, if you have strong theoretical reasons for expecting Group and Group:Time to vary by participant. You seem to indicate that this is the case.
However I would be very wary of fitting too many random slopes. This is where the advice to "Keep it Maximal" is fatally flawed - very often the data simply doesn't support such a complex random structure, and even if it did, such a random structure might be overfitted, resulting in a model that fits this particular dataset well, but does not generalise to other similar datasets.
Best Answer
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.