Help with mixed model in R

I'm trying to apply regression on my data and I would like to be sure to do it correctly. My dependent variable (DV) is the position of the subject (numeric value). My independent variables (IV) are :

• The group in which the subject is (2 groups, a subject is in one or the other)
• The type of stimulus (2 different types, each subject is confronted with each stimulus so it is a "within" variable)
• The time of the measure (each subject got measured 3 times for each stimulus, so 6 times in total) I'm interested in each principal effect and the triple interaction (not the doubles).

If I'm correct, I have 1 between-subject IV (the group) and 2 within-subject crossed IV (stim and time). My dataframe counts 6 columns:

• The NS column gives the number of the subject.
• The Pos column which gives the subject's position
• The Group column
• The Stim column (the type of stimulus).
• The Time column (the moment of measurement; coded -0.5, 0 and 0.5)

Here is the code I ran in R :

RegAlc <- lmer(Pos ~ Group + Time + Stim + Group:Time:Task +
(Time*Stim|NS), data = d)
summary(RegAlc)


The code works but I would like to be sure that this is the correct way to analyze these data.

Thank you very much!

• (+1 to @Dimitris) plus It’s unclear what Task is and why it’s only included in an interaction. – rolando2 May 23 '20 at 13:18

It is not clear whether the Pos outcome variable is a continuous random variable, resulting in error terms having the normal distribution. Note that this is an assumption behind the linear mixed model you are fitting with lmer().
• You have included the main effects of Group, Time and Stim, and their three-way interaction, without including the two-way interactions. Typically, this is not done. Moreover, interaction terms are complex terms requiring sufficiently large sample size to estimate them stably. This holds for two-way interactions, and even more for three-way ones. Are you certain that you want to include all these interaction terms?
• The random-effects part is often build using a build-up approach, starting from random intercepts, i.e., (1 | NS), then including random slopes, i.e., (Time | NS), and performing a likelihood ratio test (using the anova() function) to see if the fit of the model is improved. You could continue to include more complex random-effects terms. But note that often the dependencies in the data are not that complex to support including many/complex random-effects terms. Trying to fit a mixed model with such a complex structure may result in unstable estimated and boundary problems (i.e., the same variances of the random effects are estimated to be zero).