2
$\begingroup$

I'm struggling with modeling some experimental data using the lme4 package in R, and would appreciate input.

My experimental design is as follows: subjects entering the experiment answer a screener question, which is used to randomly assign them to a between-subjects condition (variable=rank, which has 2-levels (0/1)). They then complete a distractor task, and make two choices (choice being the within-subjects dependent variable). At each choice, the stimuli are RANDOMLY ASSIGNED and crossed by two factors (msg has 3-levels ("norm", "no norm" and "provincial"), and cost has 2-levels (0/1)). Because participants were randomly assigned to both cost and msg at two points in time, theoretically they could have the same combination of cost and msg at both points in time.

My life would be easiest if I could use a wonderful package such as ezANOVA, but my data won't allow me to do this because every individual doesn't have EVERY combination of the two within-subjects variables see here. So, I'm in the less-familiar territory of mixed models.

My hypothesis argues that there should be a three-way interaction between rank, msg, and cost. Thus, a simple version of my model might be:

m1 <- glmer(choice ~ msg*cost*rank + (1|id), data=df, family="binomial")

But, I've also seen it suggested on this site that my random effects should be modeled as follows in order to evaluate the interaction between the factor and subjects:

m1 = lmer(choice ~ msg*cost*rank + (rank|id) + (cost|id), data=df)

The latter model has me straying into unfamilar territory, so I'd appreciate any advice about how to model this data in a way that is (1) simple, but (2) appropriate.

Sample data below:

> dput(df[1:700,2:6])
structure(list(time = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), choice = c(1, 1, 
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 
1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 
1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 
0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 
0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 
1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 
1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 
1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 
1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 
1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 
1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 
1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 
0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 
1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 
0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 
1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 
1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 
0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 
1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 
0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 
1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 
1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 
1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 
1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 
1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 
1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 
1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 
0, 1, 0, 1, 0), msg = structure(c(3L, 1L, 1L, 2L, 3L, 1L, 3L, 
3L, 3L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 1L, 3L, 2L, 3L, 1L, 1L, 3L, 
1L, 2L, 3L, 3L, 2L, 2L, 1L, 1L, 1L, 1L, 3L, 2L, 3L, 3L, 2L, 3L, 
3L, 1L, 3L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 2L, 3L, 3L, 1L, 2L, 3L, 
3L, 1L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 2L, 
3L, 3L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 1L, 
3L, 2L, 3L, 2L, 3L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 2L, 3L, 
3L, 2L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 2L, 2L, 1L, 3L, 3L, 2L, 3L, 
3L, 3L, 2L, 2L, 1L, 2L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 2L, 2L, 
1L, 1L, 3L, 1L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 
2L, 1L, 2L, 1L, 1L, 3L, 3L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 3L, 
3L, 1L, 2L, 3L, 1L, 1L, 3L, 2L, 2L, 3L, 3L, 1L, 1L, 1L, 2L, 1L, 
2L, 3L, 3L, 2L, 1L, 2L, 3L, 1L, 2L, 2L, 1L, 3L, 3L, 1L, 1L, 1L, 
3L, 2L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 3L, 1L, 2L, 2L, 3L, 3L, 2L, 
1L, 3L, 3L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 3L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 1L, 1L, 2L, 3L, 2L, 3L, 3L, 
3L, 3L, 1L, 3L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 3L, 3L, 2L, 1L, 1L, 
2L, 1L, 2L, 3L, 3L, 3L, 1L, 2L, 2L, 3L, 1L, 3L, 1L, 3L, 3L, 1L, 
1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 2L, 3L, 2L, 3L, 
1L, 2L, 2L, 1L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 3L, 1L, 2L, 3L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 3L, 2L, 3L, 2L, 1L, 3L, 3L, 
3L, 1L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 1L, 2L, 2L, 3L, 
1L, 3L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 1L, 1L, 2L, 3L, 3L, 
3L, 3L, 3L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 1L, 2L, 3L, 3L, 1L, 1L, 
1L, 3L, 3L, 1L, 1L, 3L, 1L, 2L, 3L, 1L, 1L, 3L, 2L, 1L, 3L, 3L, 
3L, 1L, 3L, 1L, 3L, 1L, 3L, 2L, 3L, 2L, 2L, 1L, 2L, 1L, 3L, 2L, 
2L, 3L, 1L, 2L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 
1L, 1L, 3L, 1L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 1L, 2L, 3L, 2L, 3L, 
2L, 3L, 1L, 3L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 3L, 2L, 1L, 1L, 
1L, 2L, 2L, 1L, 2L, 1L, 3L, 1L, 2L, 2L, 2L, 1L, 1L, 3L, 3L, 1L, 
1L, 3L, 1L, 3L, 3L, 3L, 3L, 2L, 1L, 1L, 3L, 2L, 1L, 3L, 2L, 2L, 
1L, 1L, 3L, 3L, 3L, 1L, 1L, 2L, 1L, 1L, 3L, 1L, 2L, 2L, 3L, 1L, 
2L, 2L, 3L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 3L, 
1L, 1L, 3L, 3L, 3L, 2L, 3L, 2L, 2L, 3L, 1L, 2L, 3L, 3L, 2L, 2L, 
1L, 2L, 3L, 2L, 1L, 2L, 3L, 3L, 2L, 2L, 2L, 3L, 1L, 2L, 3L, 2L, 
3L, 3L, 3L, 3L, 1L, 2L, 3L, 2L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 2L, 
2L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 2L, 3L, 
2L, 2L, 3L, 3L, 3L, 1L, 3L, 2L, 2L, 1L, 2L, 3L, 1L, 3L, 2L, 3L, 
1L, 2L, 3L, 2L, 1L, 2L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 3L, 3L, 2L, 
1L, 2L, 3L, 2L, 1L, 2L, 1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 
2L, 2L, 3L, 2L, 2L, 3L, 3L, 1L, 3L, 1L, 3L, 2L, 1L, 3L, 1L, 2L, 
1L, 3L, 1L, 3L, 1L, 1L, 2L, 1L, 3L, 2L, 3L, 3L, 3L, 1L, 3L, 3L, 
2L, 2L, 1L, 2L, 2L, 2L, 2L, 3L, 1L, 1L, 1L, 2L, 3L, 2L, 3L, 1L, 
3L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 3L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 
2L, 2L, 1L, 3L, 2L), .Label = c("No norm", "Norm", "Provincial"
), class = "factor"), cost = structure(c(1L, 2L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 
2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 
1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 
2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 
2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 
1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 
1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 
2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 
1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 
1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 
1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 
2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 
1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 
2L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 
1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 
2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 
2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 
2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 
2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 
1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 
2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L), .Label = c("0", "1"), class = "factor"), 
    rank = structure(c(1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 
    2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 
    2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 
    1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 
    1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 
    1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 
    1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 
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6
  • $\begingroup$ That might not be related to your question but I am a bit confused by the “screener question […] used to assign randomly […]”. If treatment is based on the answer to some question, it's not random. $\endgroup$
    – Gala
    May 3, 2013 at 13:39
  • $\begingroup$ Hi there - you can correct me if I'm wrong, but they are randomly assigned to receive a stimulus that relates either their most important (=1) or least important (=0) issue (this is the variable rank). Whether or not the choices someone is presented with relate to their most or least important issue is thus orthogonal to the choice itself, as people have equal likelihood of being assigned to either their most (or least) important issue. Do you agree? $\endgroup$
    – roody
    May 3, 2013 at 15:51
  • $\begingroup$ It sounds reasonable, I simply misunderstood you earlier. $\endgroup$
    – Gala
    May 3, 2013 at 16:35
  • $\begingroup$ Yes, you have to specify that msg and cost are random effects in the level 1 model. You might also consider specifying the interaction of the two as random so you can examine the three-way interaction at level two with the rank variable. $\endgroup$ May 6, 2013 at 14:38
  • $\begingroup$ @toomuchpj: Hi there! Could you possibly elaborate? Is the following what you are suggesting: m1 = lmer(choice ~ msg*cost*rank + (rank|id)*(cost|id), data=df) $\endgroup$
    – roody
    May 6, 2013 at 14:40

0

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