1. The Rasch Model is not a model for data. It is a definition of
measurement.
2. Item banking is just an application of this definition.
3. The practical question is: can some data be constructed which
cooperate with the Rasch Model well enough to result in meaningful
definitions of interesting variables and useful measurements on them?
4. How is "useful" determined? The extent to which some particular
data cooperate with the intention to construct measurement is
indicated by various versions of the third statistic, fit. (The first
and never neglected statistic is the ESTIMATE, the second and
sometimes neglected statistic is the ERROR, or reliability, of that
estimate. But the relevance, or validity, of either depends on the
almost always neglected but actually fundamental third statistic,
FIT.)
No fit indicator alone, however, can suffice to define what is "useful." Even perfect knowledge of a null distribution for a fit statistic and a universally agreed upon rejection level are not enough. The bottom line is: What difference does it make?
To answer that question we must:
a. Return to the data and isolate the individual unexpected
responses that are responsible for the misfit,
b. Investigate the substantive cause of each unexpected response,
and, when no workable explanation can be developed and implemented,
then
c. Calculate how much logit difference it makes in the calibrations
and measures when the remaining inexplicable unexpected responses are
exchanged for expected ones and then
d. Think through the substantive implications of these particular
logit differences.
If, in the end, the consequent reordering of items and/or persons are meaningless, then this misfit has been shown not to matter. But, whenever a reordering is meaningful, then that uncertainty in the location of the item or person must become part of the final results. It must be kept in mind as something still not known.
What does this have to do with the threat to item banking of interactions between exposure and item difficulty? Once the specifics of an interaction, or readiness effect, have been identified, it would seem reasonable to restrict calibration of the items involved to persons who are thought to be ready and to delete (change into missing) responses to these particular items produced by persons who are thought not to be ready. Of course the identification of readiness cannot be perfect, but information about school, grade, text and testing date ought to help, especially when joined with a list of the persons and items who have produced unexpected responses.
Useful measurement through concurrent equating and one-step (concurrent) item banking. Wright BD. … Rasch Measurement Transactions 2:2 p.24
Useful measurement through one-step (concurrent) item banking. Wright BD. … Rasch Measurement Transactions, 1988, 2:2 p.24
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