How can I program a model with R to evaluate the interaction between a within-subject effect and a continuous variable at the subject level?
Scenario: 62 subjects did a selection task composed of 128 items, that can be divided into four conditions, because each item has a cue and a target (also other options but thats not of interest in this analysis) which can be affectively positive or negative (2x2 factorial design, within-subject). I found a significant within-subject effect hinting that cue-target affective incongruence difficults performance (accuracy is my dependent variable). Now, here comes the issue: I also measured with neuroimaging the integrity of a certain area of interest in the brain. So I have a continuous variable at the subject level. The hypothesis is that this area is responsible for solving cue-target incongruent tasks.
I have one single value for each subject. It's a measure of white matter integrity for a single region. The possible minimum and maximum of this measure are 0 and 1 because of how its computed, but the values for this region, for this subjects goes from .37 to around .48. What I want to do know is evaluate the interaction between the within-subject effect in accuracy and this continuous variable. I'm aware this requires a multilevel analysis (I'm using R), because I have to analyze the subject and the item at the same time.