Rasch Measurement Theory

Rasch Measurement Theory (RMT) arises from the work of the Danish Mathematician, Georg Rasch, and the development of the Rasch model for facilitating the conduct of item analyses now known generally as a Rasch analysis.

The Rasch Measurement model, where the total score — the sufficient statistic — summarizes completely a person’s standing on a variable, and arises from a more fundamental requirement: that the comparison of two people is independent of which items may be used within the set of items assessing the same variable.

In this context, sufficiency makes conditional estimation possible, which means that the distribution is irrelevant if the measurement criterion, that is, invariance, is met: the reason is that the person parameters can be eliminated to estimate the item parameters.

Equally important is that, due to uniform threshold discrimination in the dichotomous and polytomous modes, it is possible to estimate relative to a unit in Rasch models: there is no measurement without estimation of magnitudes relative to a unit.

The aim of a Rasch Measurement Model analysis involves the construction of a variable for revealing how much more or less of the concept under review a person possesses or reveals. This is analogous to helping construct a ruler, but with the data of a test or questionnaire involved directly.

A Rasch Measurement Model analysis provides evidence of anomalies with respect to the operation of any particular item, the presence of differential item functioning (DIF) with any item, or the statistical independence of the items involved in the instrument.

If anomalies do not threaten the validity of the Rasch Measurement Model, or the measurement of the construct, then people can be located on the same linear scale as the items.