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I have built an GPCM IRT model using survey data, but have found significant local dependence (in violation of the LID assumption) using residuals() in R. I've found information online for dealing with LD in Rasch models-- you can combine them into super-items, which makes them polytomous.

Can I do this with polytomous data? What exactly does this mean (is it an item with no question and 10 response categories?)

Finally, how do you know which items to combine? Unfortunately, nearly all of my items are scoring high with more than one other item. I did use EFA (and MIRT) to see whether perhaps I was missing a dimension, but I can't seem to find anything significant.

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From what you've described, my inclination is that you have item redundancy. Look at how highly correlated the flagged polygamous items are. If they are highly correlated, then you can consider just dropping one (or some) of the redundant items.

Additionally, if you wish to check if this is a reasonable approach, run the models with different items from the subset and then compare the ability estimates for each individual. If they are very highly correlated, then you probably have redundant items.

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    $\begingroup$ Good instincts and good call! I have some that can be seen as redundant. I (think?) can't drop them, though, because some people answered one, some answered the other, and some answered both. $\endgroup$ – karen Mar 27 '18 at 23:05

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