# Clustering and interactions in a multilevel model in R

We are conducting an individual participant level meta-analysis on a series of clustered randomised controlled trials, where we are mainly interested in an interaction effect with a characteristic (whether students have had contact with a particular kind of service). In essence, there are two things we need a multilevel model for:

• Dealing with the nested clustering - in this case schools within trials
• Producing an interaction effect with the random effects for the trials

The data is unfortunately protected from being shared but the structure is:

• Outcome variable - test scores (score)
• Trial - which trial a person appears in
• School - this is the level the trials were randomised on, so it is nested below trial
• Service - another individual-level characteristic that we want to interact trial with

If we had a fixed effects model then this would look something like:

lm(score ~ trial*service, ...)


if we just ignored the nested clustering (where trial is a factor variable for the treatment arm and which trial it is in).

If I could ignore the interaction then in lme4 it would be something like:

lmer(score ~ (1|school/trial), ...)


but what I would like to see is how to interact that with service, which maybe I could do by setting:

lmer(score ~ (1|school/trial/service), ...)


but feel this is wrong as service is an individual-level characteristic, so its weird to put it "above" school or trial in the clustering.