What Use Are Rasch Measures?

Question: I've spent a lot of time and effort estimating Rasch measures. Now what do I do with them?

Reply: Rasch measures can be used wherever person raw scores and percentages or item p-values would be used in conventional test reporting and statistical analysis. Rasch measures have the linear properties that most statistical routines (and non-specialist readers) assume of your numbers, but which raw scores and p-values don't have. So you can use Rasch measures for reports, plots, descriptive statistics, statistical tests, regressions, etc. A powerful use of Rasch measures is to draw pictures (item and person maps) which show the item hierarchy (the construct validity) of the items, and the person hierarchy (the predictive validity) of the persons.

The hierarchy of item difficulties is especially important because it defines what is being measured, the measurement ruler. Does the ordering of the items in difficulty match the intentions of the instrument developer and the expectations of those planning to use the test results? It is yet more instructive if, prior to data collection, the test development team sketch out the intended difficulty order of the items. This can then be compared with the order estimated from the data. The comparison usually confirms most of the intended ordering, so supporting the validity of the test. But the comparison may also point out an item or two that were supposed to be easy but are not, and vice-versa. This leads to a better understanding of the underlying construct, the latent variable, and also to improvement in the items. When an a supposedly easy item is reported to be difficult in practice, this can also indicate an area where better education or training is needed of those for whom the test or assessment is intended.

For instance, in the Knox Cube Test (a standard dataset, Wright & Stone, 1979), a gap in the item hierarchy indicates where new items should be written to target the sample. The item hierarchy also indicates how "number of taps", "number of reversals", and "length of sequences" affect item difficulty, so leading to a better understanding of how we store information in our short-term memory. Item difficulty measures are important if the instrument is to be used for setting criterion-level cut-points. They are also crucial for equating instruments, and for selecting items for adaptive administration.

What Use Are Rasch Measures? … Rasch Measurement Transactions, 2007, 21:2 p. 1104

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
in Spanish:	Análisis de Rasch para todos, Agustín Tristán		Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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