I've conducted an experiment in which 20 pairs of talkers are conversing in their first and second language (L1 and L2, respectively) both in quiet and in noise in a fully crossed design:
- L1 in quiet
- L1 in noise
- L2 in quiet
- L2 in noise
Each pair is replicating the experiment three times. Therefore, I have three fixed effects: background (levels = quiet, noise), language (levels = L1, L2), and replicate (levels = 1, 2, 3). Furthermore, I have a random effect of pair, talker and gender. This is where I need some help to understand the nested vs crossed structure of the random effects. I have 20 pairs making up a total of 40 talkers (labeled talker 1:40). Each of those talkers has a gender. I'm assuming there's a correlation between the outcome measures within the pairs, so that talker 1 & 2 show correlated behavior that's uncorrelated with talker 3 & 4. Which one of these models would be correct (if either)?
- y ~ background * language * replicate + (1 + background + language + replicate | pair) + (1 + background + language + replicate | person) + (1 + background + language + replicate | gender)
- y ~ background * language * replicate + (1 + background + language + replicate | pair/person/gender)
The latter model fails to converge. I have 480 data points in total.