# Useful measurement through concurrent equating and one-step (concurrent) item banking

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

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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