I know just enough about
lmer() to get myself by with simple models, and to get myself into trouble with more complex ones. I'm really confused about the proper way to model some data I'm currently working with, and would be grateful for some help.
The question: do people give different estimates of a distance after being fatigued by exercise, and does ingesting sugar during the exercise change the relationship?
The setup: participants are shown a sequence of 3 targets at different distances, and asked to provide a distance estimate for each. They then exercise for a while, and then make 3 more distance estimates to 3 new target distances. This whole procedure happens twice for each participant, on separate days, and one day they ingest sugar, while on the control day they do not.
Here is the data:
DV: Distance estimates
Actual distance: 6 possible distances
Condition: 2 level factor: treatment/placebo
Measurement occasion: 2 level factor: Pre/Post exercise
So, for each subject, I have:
3 distance estimates before exercising w/ sugar, 3 distance estimates after exercising with sugar, 3 distance estimates before exercising w/out, and 3 distance estimates after exercising w/out.
Ultimately, I'd like to know if the estimates people make post-exercise are different depending on the Condition, but those estimates should also be dependent on the starting point of Pre-exercise estimates. Since the actual target distances before and after are different, I can't do a direct comparison (the means of each group of 3 are the same, however).
The thing that is tripping me up is that both factors are within subjects. I have repeated measures at different levels (repeated estimates in each state, repeated estimates separated by time, and repeated estimates separated by treatment) and I'm not sure what to treat as fixed effects and what to treat as random effects, whether I have a nested structure or not, and whether I should be looking at random intercepts only or also random slopes (and for which variables).
Any help or suggestions are greatly appreciated. Thanks!