My group recently ran an experiment where participants completed 10 trials of a task with 5 repeated measures observations within each trial. We are interested in examining the growth processes within each trial as well as across trials (but still within individuals). In HLM terms, we have a 3-level dataset, with level-1 representing the within-trial level, level-2 the between-trial level and level-3 the between-person.
I'm wondering how MPlus will handle the fact that levels 1 AND 2 are repeated measures. Can Mplus perform a 3-level HLM-type multilevel analysis? Is this even appropriate here?
We'd also like to account for autocorrelation at both of the repeated measures levels. Can autocorrelation only be examined using the multivariate growth modelling approach? If this is the case and we were to use a TYPE = COMPLEX analysis, does that mean that only the within-trial level will be analysed using the multivariate approach and the between-trial level will be analysed using the univariate approach? What are the implications of this?
The most complex approach would be to model it as a single-level, doubly wide analysis where you have 5 x 10 = 50 variables. You can then have all kinds of autocorrelations (see the UG for autocorrelation modeling using Model Constraint). Here you could formulate 10 growth models where the 10 sets of growth factors are related in some way - for example the intercept growth factor could have a growth model over trial, and so could the slope. This approach would require a sufficient sample size.
An alternative is to simplify. If you drop the autocorrelation on the trials level (middle level) you can model this as a 5- variable wide twolevel model where the cluster variable is the individual and the trials are the observations within individual. You can evaluate the autocorrelation between trials using factor scores. Alternatively you can create a within level predictor such as the average of the previous trial and use it in the growth model for the within level - that also takes care of the autocorrelation on the trial level. Of course you can model the autocorrelation on level 1 with model constraints.
Hi Bengt, To give you a bit more information about the model I'm trying to test, the primary purpose is not to model the growth, rather to control for it when assessing the influence covariates. At both the between-trial (middle) level and the within-trial (lowest) level, we have six variables at each time point that form a mediation chain. So at each level we have a model that might look like
a -> b -> c -> d -> e -> f
So if running a doubly wide growth model with 50 outcome variables, we would also have to include 5 x 50 = 250 covariates. I'm guessing this is not even feasable with a sample size of just 130 at the highest level?
In that case, I'm interested in running a multilevel growth model as you suggested aboce. This would essesntially collapse across trials and reduce the number of variables in my model to 30 or so.
The only issue with this would be controlling for autocorrelation at the between-trial level. You suggested creating a variable that represents the score at the previous time point and controlling for it. The problem I'm getting with this is that including these lagged variables in my model creates a lot of misfit.
The other option you suggested would be to evaluate autocorrelation using factor scores. I'm not familiar with this method, would you be able to give me a bit more detail about how this can be done?