# Four Introductions to the Rasch Model

The greatest challenge to practitioners of Rasch measurement is not test construction or analysis, but communication. The most clear-cut and insightful findings are valueless if the intended audience are baffled or, worse, antagonized by the method used to obtain them. Let us review four Rasch measurement introductions with a view to enhancing our own endeavors to explain Rasch measurement.  The shortest at 9 pages is Snyder & Sheehan (1992). They include no mathematical formulae, but take a page to recite the operation and specifications (incorrectly termed "assumptions") of the model. They describe three functions of Rasch analysis: item banking (with a useful table of benefits), test analysis and person measurement. Three tables of measures are included that beg to be plotted - see the "Bayley Mental Scale" Figure for a plot of their Table 2 with a "best fit" line added. In discussing person measurement they emphasize that a focussed subset of items is as informative as an entire test, but speedier and less of a burden. This introduction is sketchy, but is informative for a beginner.

Next in length at 12 pages, and a little more mathematical, is Hawkins (1987). She commences with an explanation of latent trait models and a plot of ICCs. The Rasch model is introduced as merely a "one-parameter" simplification. Her example concerns two versions of the same 75 item MCQ test. The two calibrations for each item are tabulated and discovered to have a correlation of .91. Does this summary statistic confirm Rasch objectivity? A plot with confidence bands would have told all - see Figure showing Hawkins' data. Finally, she discusses how to use test information curves to aid test construction. This introduction will mislead, rather than assist, a neophyte.

Longer at 18 pages and more complex De Ayala (1993). This is a mathematically sophisticated introduction to ordered and nominal logit-linear response models, including models algebraically similar to, but conceptually far from, Rasch models. De Ayala expects the reader to follow a sequence of algebraic manipulations, and also to understand matrix notation. This introduction is for psychometricians only.

Longest at 40 pages, oldest and in German, but included as a contrast, is Stene (1968). This introduction is close to Rasch (1960/1980) in content, algebra and style. It is a convenient summary of Rasch's algebra. Stene also presents a "practical example" that demonstrates pair-wise estimation of item calibrations, along with a graphical investigation of fit. Rasch measurement, a theory often shrouded in algebraic confusion, is revealed by Stene to be a useful and practical tool for any test constructor with a pocket calculator and a sheet of graph paper. Writers of Rasch introductions would do well to build on pages 255-263 of Stene's chapter.

John M. Linacre

De Ayala R J 1993. Methods, plainly speaking - an introduction to polytomous item response theory models. Measurement and Evaluation in Counseling and Development. 25(4) 172-189.

Hawkins K W 1987. Use of the Rasch model in Communication Education: an explanation and example application. Communication Education 36(2) 107-118.

Snyder S & Sheehan R 1992. Research methods - the Rasch measurement model: an introduction. Journal of Early Intervention 166(1) 87-95.

Stene J 1968. Introduction to the Rasch theory of psychological measurement (in German). Chapter 9, 229-268, in G.H. Fischer (Ed.) Psychologische Testtheorie. Bern: Hans Huber.

Four introductions to the Rasch model. Linacre JM. … 1993, 7:2 p.290-1

Four introductions to the Rasch model. Linacre JM. … Rasch Measurement Transactions, 1993, 1993, 7:2 p.290-1

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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