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I am estimating a mixed logit model with hierarchical Bayes procedures to deal with my categorical data. I am wondering if I'm representing the data correctly.

The data comes from experiments where participants are shown constructed images and need to identify if the image is constructed from information of type A or type B. After each choice the participant makes, they are additionally asked to rate how confident they are that they have answered correctly using a 7 point likert scale. Each subject makes this classification of type A or type B for a series of images and rates their confidence each time.

In my model, I encode the choice as having 2 alternatives: either the image was correctly identified or it was not. Previously, I thought perhaps I should encode each choice as having 14 alternatives ranging from strongly confident correct answer to strongly confident wrong answer. (Or that I should do it as a nested choice as mentioned in section 6.3 of this: elsa.berkeley.edu/choice2/ch6.pdf)

However, I now have doubts because what I'm really interested in is what variables are relevant to a subject's ability to make a correct identification of the image type. Since the Bayesian procedures allow me to estimate covariance among all random coefficients, is it perhaps more reasonable to encode the likert rating not as part of the choice alternative but as one of the (random coefficient) variables? Is that even a valid approach? Should I revert to my 14 level approach?

Is there something else I should be considering?

Thanks very much for your help.

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It's difficult to speak on the issue without much domain knowledge, but I think that the most interesting model would be the one you're thinking about: estimating the 'effect' of subject confidence. Certainly there's nothing wrong about doing this from a statistical point of view, especially if you believe that there would be correlation among confidence and other predictors (as you seem to think). It's also like to assist your model's characterization of its own uncertainty. I also think a 14-level outcome would be unnecessarily complicated & complex for what you're trying to do, especially computationally.

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