I'm having a hard time figuring out the appropriate fixed and random effect structure for my model and would appreciate some help. In my study the frequency of two environmental behaviors was assessed across three time points. Participants intended to increase one of those behaviors while they didn't intend to change the other one. In addition self-control was assessed. An example data set for one participant looks this:
So, I have six rows for each participant, all participants are in both the intention and no-intention group, which makes it a within (or crossed) design.
- time points are treated categorically (altough I consider changing that as not everyone responded at the same time)
- the frequency of environmental behavior and self-control were assessed on Likert scales (1 - 5), so are not really continuous either.
I want to assess
a) the effect of intention on whether participants increased their behavior or not. I expect intended behaviors to increase (positive slope) and non-intended behaviors not to change (no significant slope).
b) the effect of self-control on the increase of environmental behavior, so a self-control x time x environmental behavior interaction.
a) should be the primary focus here, because I don't know how to account for the within-design structure in my model. I'm working with the lmer function in R.
I have to account for a random intercept and slope of ID, as I am expecting participants to have different baselines and developments. So I would start with:
m1 <- lmer (eb ~ time + int ( 1 + time | ID), data = d)
In addition, I should be treating intention as a grouping variable, so I should include
( 1 | intention).
m2 <- lmer (eb ~ time + int ( 1 + time | ID) + (1 | intention), data = d)
How do I account for the fact that all IDs are in both groups? Do I have to account for that intention is not changing over time? Which other random effects should be included? I have read through a lot of literature, but can't really find an example that is similar to mine. I have played around a bit with different models, but I'm really lacking an understanding of what I'm modelling with different random effects.