One impediment to acceptance of the Rasch model as a viable method of measurement in psychology and education has been the concept of fit.
Fit implies meeting requirements or matching intentions. The concept is well accepted in the everyday and the physical science worlds. When a tape measure appears stretched, it is rejected and another found. When one wishes to measure the circumference of a cylinder, one seeks a measuring instrument pertinent to the job. We use micrometers to measure small distances, pedometers and transcepts to measure large. The concept of fit is well known to statisticians. Tests of fit are powerful tools which enable statisticians to make objective, yet qualified inferences. It is normal practice to match the measured and the measure.
But when it comes to using the Rasch model as a method of measurement, the concept of fit is not accepted. "How dare we reject some items or some persons? One must never tamper with the test. That is manipulating data which is not acceptable." Maybe "one" should take a second look.
The Rasch model is stochastic. It asserts that the data depend on probability, not certainty. When an event has a high probability, that does not mean it will definitely take place. We are, nevertheless, surprised when highly probable events persist in not occurring. The concept of fit is a natural consequence of any stochastic model. It specifies an indication of the match between a group of persons and a set of items. If for any reason a few persons from the group or a few items from the set do not perform as expected, these will be flagged as persons or items differing from expectation and therefore misfitting. Fit indicates the validity of the item calibrations and the person measures. Far from being unacceptable, fit is the essential gauge of the performance validity of the test content/construct in the circumstances in which it is used.
The Rasch model is a useful idealization of reality. Some misfit is to be expected. We know from practical experience that person raw scores do not exhibit invariance. The stochastic Rasch model actually fits our own expectations very well. Do not reject this useful model on a misunderstanding of intention.
Fits about "Misfit", F Shaw Rasch Measurement Transactions, 1991, 5:1 p. 132
|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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