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

Please help with Standard Dataset 4: Andrich Rating Scale Model

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

To be emailed about new material on
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from welcomes your comments:

Your email address (if you want us to reply):


ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website,

Coming Rasch-related Events
April 26-30, 2017, Wed.-Sun. NCME, San Antonio, TX, - April 29: Ben Wright book
April 27 - May 1, 2017, Thur.-Mon. AERA, San Antonio, TX,
April 29, 2017, Sat., 16:35 to 18:05. NCME Presidents Invitational Symposium: a new book commemorating Ben Wright's life and career, 16:35 to 18:05, San Antonio, TX,
May 26 - June 23, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 30 - July 29, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil,
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia,
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia.
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan,
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago,
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
The HTML to add "Coming Rasch-related Events" to your webpage is:
<script type="text/javascript" src=""></script>


The URL of this page is