As a psychologist and not a statistician, I have always used ANOVAs to perform analyses on repeated-measures designs but have since learned you should instead use mixed linear modeling with these type of experiment to deal with the (pretty much inherent) sphericity violations that come with them. As such I'm trying to re-run all of my analyses appropriately using this new technique. As someone with a horrific math background, please bear with me as I try to garner some insight into how to correctly create a model because I have no guidance here but am reading as much as possible and trying really hard.
I have an experiment with the following set-up:
I have two different groups of subjects - TU and RU. This is a between-subjects factor.
Each subject (regardless of group) is exposed to 3 different stimuli - CS+, CS-, and CST. This is a within-subjects factor.
Each subject (regardless of group) is exposed to 2 different MRI scans - Temporal scan and Compound scan. This is a within-subjects factor. I don't know if this is important but: During each scan they see different physical shapes. Also during each scan the seem the same TYPES of stimuli; however, whereas the CS+ and CS- are essentially the same during each scan the CST is different between scans (i.e. it is associated with 100% shock during the temporal scan but only 50% shock in the compound scan).
During each stimulus presentation we are measuring the dependent variable at each of 12 timepoints - sec1, sec2, ..., sec12. This is a within-subjects factor.
We have collected 3 other variables we are hoping to control for:
- Sex (M and F)
- STAI-T anxiety scores
- STAI-S anxiety scores
The dependent variable is rating where they rate how likely they are to be shocked at that point in the trial.
I have not collected any participants in the RU group as of yet so I am avoiding the groups variable at the moment.
I'm using R's
lme4 to create my model so my first problem is figuring out what are fixed versus random factors in this scenario. So far I believe the following to be true.
Stimuli, scans, and timepoints are all fixed factors. The stimulus manipulation is our main manipulation. We are also hoping to investigate the difference between the "same" stimuli during each scan (i.e. between the CST in the temporal scan & the CST in the compound scan, etc.) so scan is a fixed factor as well. While it might seem weird to have timepoints as a fixed factor, one of our hypotheses regards where in the trial the ratings differ between each stimulus so that's why I'm considering timepoints a fixed factor.
In terms of random factors - I'm almost positive subject is a random factor. It's the only random factor I'm basically sure of.
My confusion is mostly regarding whether to consider the remaining variables - specifically the STAI scores - fixed or random. I am using this book as a basis for my learning and am slightly confused. Essentially I DO want to know how sex, STAI-S, and STAI-T scores affect ratings but they were not the variable of interest nor were they manipulated. I BELIEVE all three should be considered random factors. According to the book linked above the variables might fit the criteria for fixed factors for the following reason: Our subjects are screened to not have anxiety disorders. The STAI is not a measure of clinical anxiety so, while subjects have the potential to score any value on the STAI tests, I'm ultimately not going to be able to generalize data to the entire population. According to this post here though, these seem to fit more with random effects since I would expect to get different values if I ran the experiment again and, while it would be interesting to see the effects of the scores on the ratings, the main point of including them in the model is to ACCOUNT for them, so perhaps they should be random?
Can anyone give insight on if I'm moving in the right direction with all of my variables? Ultimately I know I'll have questions about nested/crossed factors and what the ultimate model should be but this is my starting place.