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I have a data set where n participants were asked to give a yes or no response to of 12 different (and distinct) stimuli. Each stimulus fits into 1 of 3 categories and an item for each category appears 4 times.

This all fits neatly into a 3x2 contingency table, but each participant is contributing to the table 12 times! I would compare categories with a chi-square test, but the assumption of independence is broken.

Are there alternatives that would account for this? Should I be looking at totaling the responses into 0 to 4 scores?

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I would try to model this using multivariate logistic regression. This can probably be fit in R with lme4::glmer, some information is at Fitting multivariate linear mixed model in R, follow the links and references therein!

This would need a random intercept for each respondent, shared among the 12 logistic regression, so would really be a multivariate model.

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