Linking a three level variable with a binary score to predict total score

I have (what I'd like to be) a continuous dependent variable (DV =
percent correct of dichotomously scored items on a listening test,
where 1 is correct, 0 is incorrect) and several predictor variables.
The key interest is seeing how well listening accuracy with
individual words (isolated speech) predicts listening accuracy with
sentences (connected speech). Listening perception can be confounded
by association (?Assn_status? in Sample Data). If a word isn?t known
or isn?t readily associated with the context, it may be perceived as
another word. Accurate perception is further influenced by the
listeners first language (L1). The equation would be:

connected speech ~ isolated speech + association + L1 + 1|participant +
error

The snag is that association (categorical, three levels) is different
for each person, and I need to index the participants? individual
associations for each item with their score on that item. It is
unclear to me how to do this, though I've tried what seems an
infinite number of equally futile options. It may be that I have to
toss the idea of the continuous DV and go with a logistic regression.