[R-sig-ME] Linking a three level variable with a binary score to predict total score

[Stuart Luppescu]

On Tue, 2021-01-26 at 02:34 +0000, Johnathan Jones wrote:
> 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.

I can't really comment on the model (it is outside my area of
expertise) but I really think using percent correct as an outcome
variable is not the way to go. I would analyze the individual responses
in an IRT model (I, personally, belong to the Church of Rasch) and then
take the person measures from that analysis and analyze them in your
lme model or whatever. 

I think you can also do something similar in lme or lmer by using the
individual item responses (0, 1) as the outcome with a logit link, and
include an item indicator for each response, nest them all within
individuals, add your other predictors, and model them that way.

If you don't want to do IRT or the other way I suggest, at least
convert the percent correct to log odds and use that as the outcome. 

-- 
Stuart Luppescu
Chief Psychometrician (ret.)
UChicago Consortium on School Research
http://consortium.uchicago.edu