[Rasch] about invariance

Agustin Tristan ici_kalt at yahoo.com
Mon Nov 5 04:00:52 EST 2007

  Following the standard procedure to get the scale of a test (measures in logits vs number of correct answers), we know that two persons answering correctly M items of a single test with N items, will have the same measure B in logits (but different fit), independently of which items were answered by each person.
  I've shown this to my colleagues, but one indicates he gets different results for two persons with 4 correct answers in a 10 items test, if person (a) answers only the 4 hard items and person (b) answers correctly only the 4 easy items. He promised me to send an explanation.
  Has somebody found this result that does not correspond to what the Rasch model (or IRT) may explain? How can it be done if possible? This does not correspond to invariance!
  I've seen RMT, winsteps manual, the book by Hambleton and the notes from my course with David Andrich, but I don't have a solution.

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