Hi @martinmodrak and @Solomon,

Finally getting back around to responding to this - thanks a lot for your thoughts, I appreciate it. For reference, I’d like to fit a full model, but I think that might be a bit tricky (so far, I haven’t managed to get very clean results).

The data-generating story is this:

Each of 30 participants completes a series of binary trials of a task (let’s call it the “word formation task” for now), which have two subtypes, the outcome of which is of primary theoretical interest. Theory predicts that two internal qualities should influence their responses, one quantity for one subtype, and another for the other.

After the trials of the binary task, each participants completes a different task (30 trials of two different subtypes, let’s call it the “word rating task”) which is predicted by theory to be predicted by the internal qualities which were predictors in the previous task.

The goal is to be able to model the correlation between word-formation task and the word-rating task, both at the population level and at the level of the individual, for each of the two subtypes of trial which measure the two internal qualities. The word formation task has a binary response variable which is predicted by other factors in addition to this internal quantity, and the word rating task is a five-level ordered dependent variable (Likert scale data), where the only theoretically expected predictor is the internal quantity.

edit: What I’ve done is extracted by-participant (posteriors for) predicted values of the BLUP for each subject from both tasks, and was trying to use these as inputs to a correlation (hence the above question), However, I can’t quite think of a great way to do this in the “fit one big model” approach. Do you guys have any suggestions on how to proceed?

(also, as an aside, I’m a *huge* fan of your books Solomon :) :) :) they’ve really helped me in getting to grips with some of the practical data wrangling that you can / need to do when fitting more complex models)