Repeated measures dyadic data with lme4

Question

I want to analyze data from an experiment where participant’s performed a task sitting next to each other. Each participant is assigned to only one dyad. Both participant's performance (dv, continuous) on the task was measured. My hypothesis concerns a cross-level interaction of an experimental factor (condition) that was manipulated within participants and a factor (role) manipulated between participants but within dyads (so participants in the dyads are also distinguishable by this factor).

The data structure looks as follows:

     participant     dyad   condition  role   dv
 1              1     2           1      1   284
 2              1     2          -1      1   290
 3              2     2           1     -1   262
 4              2     2          -1     -1   266
 5              3     3           1     -1   287
 6              3     3          -1     -1   292
 7              4     3           1      1   314
 8              4     3          -1      1   300

From what I understood about repeated measures dyadic designs from e.g., West (2013) Repeated measures with dyads, my data structure has these characteristics:

• participants are nested in dyads
• condition is crossed with participants
• participants are nested in role and role is crossed with dyads

I thought to analyze this with a mixed model looking like this

model <- lmer(dv ~ condition * role + (1|dyad) + (1|dyad:participant), data)

I am unsure, however, whether this correctly models all the intra-unit dependencies that may occur in this data? If not, what would be better way to model this data?

Answer 1

The model looks good to me, provided that you have sufficient dyads, but I would make the following minor remarks on your question:

condition is crossed with participants

participants are nested in role and role is crossed with dyads

condition and role are fixed effects, so it doesn't really make sense to talk of them as being crossed or nested. There is nothing really wrong with it, but it can cause confusion when thinking about crossed and nested random effects (where both factors are grouping variables). The software doesn't care about nesting or crossing where one of the factors are fixed.