I am not sure if this belongs in Growth Modeling or here, but since my question has more to do with understanding multiple levels, I believe my question should go here.
Here is my situation, simplified:
Subjects were exposed to an intervention (or none) on the first day of the week for 4 weeks (i.e., treatment was received 4 times). Each week is essentially treated as a new beginning, so time starts at 0 on Monday (going by increments of 1 and ending at 6 on Sunday). Weeks are also measured as time points, beginning at 0 and ending at 3. Furthermore, all subjects complete the same tasks (with continuous and categorical outcomes) every day for the entire 4 weeks.
That said, I have days nested within weeks and weeks nested within people (who are modified by treatment). This is, at least conceptually, a 3-level model.
I want to examine changes within weeks and between weeks.
I have been looking to example 9.21 within the Mplus 7 User Guide (THREE-LEVEL PATH ANALYSIS WITH A CONTINUOUS AND A CATEGORICAL DEPENDENT VARIABLE). I am not sure how I should go about defining my clusters and within variables. When I try to cluster Days within Weeks (under the between command), I get an error since Days vary within the cluster.
Should I instead be thinking of this as a two level model, with Days and Weeks both as within-subject variables?
Yes, the same subjects are always either in the intervention or no intervention group. Again, just to be clear, the intervention is repeated on the first day of each week.
Currently my data is in long form, so it looks something like the data set below.
S is the subject number, C is a Between subject variable (i.e., intervention), W and D are Week and Day, respectively, V is the assessment version given on that day (Between Day, within subject variable), Rt is the continuous outcome and Ac is a categorical outcome.
Hard to say without digging deeper. You could perhaps do it as super-wide with number of dependent variables being days x weeks x 2 (Rt and Ac), so variation is across subjects.. Or less wide with number of dependent variables on Within being days x 2 (so Within is variation across time), and Between is variation across subjects.
I was afraid you'd suggest doing wide formatting, since my actual data, using the terms of my days/weeks analogy, has 12 "weeks" (referred to as "sets" in my data) each with 160 "days" (referred to as "trials") for each week. That makes the task of doing super wide out of the question and less wide still a bit cumbersome. I'll see what I can get out of Multilevelnet.
Do you think it would be legitimate to do this as a two level model with weeks, days, and version all as Within subject variables, and treatment condition as my between subjects variable?
To answer your question, we are interested in growth over the weeks as a function of the intervention, so days are not interchangeable. Also, we are interested in looking at the effect of the intervention on growth across weeks.
I believe what is happening is that we have two levels of time (days within weeks), both as within-subject variables.
I apologize, I believe I made a typo. What I meant to say was that we are interested in growth over the days of the weeks as a function of intervention, so days are not interchangeable. Everything else I said should be correct.