Question: I combined locally-dependent dichotomous items into polytomous "testlet" items. The item-fit statistics look good, but within the polytomous items some of the Andrich thresholds are disordered. Collapsing categories made the item-fit worse. What should I do?
Answer: Ordered thresholds are relevant and central when you have an item format in which the categories are intended to reflect order. However, when you form testlets, you no longer have that situation. You have another structure in which there is no reason for the thresholds to be ordered. In fact, the more local dependence you have accounted for with the testlet form, the more the thresholds will be disordered.
It is good to hear that when you tried to correct the order of the thresholds in this situation, that you got worse fit. This is because in your situation, disordered thresholds are not showing anything wrong - they are reflecting the amount of local dependence.
Although I did not call the collection of items testlets, but just subtests, I discussed this in Andrich, D. (1985). A latent trait model for items with response dependencies: Implications for test construction and analysis. In S. Embretson (Ed.), Test design: Contributions from psychology, education and psychometrics. Academic Press, New York. (Chapter 9, pp. 245-273.)
See also Andrich, D. (2006) Item discrimination and Rasch-Andrich thresholds revisited. Rasch measurement Transactions. 20 (2), 1055 - 1057.
David Andrich, University of Western Australia
Testlets and Threshold Disordering, David Andrich ... Rasch Measurement Transactions, 2011, 251:1, 1318
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