Question: Each time I re-analyze my data after removing a misfitting item or person, another item or person misfits. When do I stop?
Answer: You need to ask yourself a practical question: Why am I removing items and persons? Is this your answer? "To improve the measurement of the persons!"
OK - then here is a strategy. (Look at underfit/high mean-squares before overfit/low mean-squares.)
1. Estimate the person measures from the original analysis. Remove whatever persons and items you see to be really, really bad.
2. Estimate the person measures again. Cross-plot the person measures from 2. against those from 1. Are there any noticeable changes that matter to you?
No. Then the really, really bad wasn't so bad after all. Keep everything. Analysis 1 is what you want.
Yes. Now remove the really bad persons and items.
3. Estimate the person measures again. Cross-plot the person measures from 3. against those from 2. Are there any noticeable changes that matter to you?
No. Then the really bad wasn't so bad after all. Analysis 2 is what you want.
Yes. Now remove the somewhat bad.
4. Estimate the person measures again. Cross-plot the person measures from 4. against those from 3. Are there any noticeable changes that matter to you?
No. Then the somewhat bad wasn't so bad after all. Analysis 3 is what you want. Stop here.
Yes. ..... (and so on)
If you must report all the persons or items, anchor (fix) the good measures at their final good values. Reinstate everything that you need to. Reanalyze and do your final reporting. The good items and person are anchored so that the bad stuff will not distort their measures.
You may discover that the conventional fit criteria are much too strict and are strongly influenced by the misfit of only a few observations.
Later: "removing the misfitting items only improved the results in the case of severe multidimensionality and large proportion of misfitting items, and deteriorated them otherwise."
in "Investigating the Practical Consequences of Model Misfit in Unidimensional IRT Models", Daniela R. Crisan, Jorge N. Tendeiro, Rob R. Meijer, Applied Psychological Measurement, 41, 6, 439-455, July 2017
Linacre J.M. (2010) When to stop removing items and persons in Rasch misfit analysis?, Rasch Measurement Transactions, 2010, 23:4, 1241
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