Theoretical Prediction of Test Items

The Lexile theory of readability measurement is attempting for reading comprehension what Newtonian mechanics achieved for astronomy. Initially, the Ptolemaic system of eccentric circles and epicycles described the motions of the planets more precisely than Newtonian mechanics. Newtonian mechanics, however, embodied a strong predictive theory which identified discrepancies for investigation and explanation. Explanations included telescope misalignment, the influence of unobserved planets (Uranus, Neptune), and short-comings in Newtonian theory (orbit of Mercury, since explained by Einsteinian relativity). The Ptolemaic system of making the model fit the data would have discovered none of these. Once established, however, Newtonian mechanics went far beyond astronomy, transforming physics and enabling our modern world.

Lexiles simplify the complex, content-ridden process of reading comprehension into two abstract, content-free components: syntactic load (quantified by sentence length) and semantic demand (quantified by word frequency). Even though reading experts insist that lexiles are a hopeless over-simplification, empirical work with Lexiles demonstrates that lexile theory-based item calibrations produce reading comprehension measures as accurate as any observational data-based calibration.

Theoretical and empirical lexiles

The Figure shows the relationship between lexile-theory and data-based calibrations for 200 sentence completion test items. The data-calibrations are in logits, rescaled to follow an identity line. In this relationship (which gives equal weight to theoretical and empirical values), the standard deviation of empirical values around the theoretical values is 177 lexiles (about 1 logit). Though departures from the identity line invite investigation, their impact on practical measurement with tests of reasonable length is negligible (see Wright & Panchapakesan, 1969).

Because of findings like this, several U.S. States are using lexiles as a fair and practical method for equating nationally published and locally produced reading comprehension tests.

Wright B.D. & Panchapakesan N. 1969. A procedure for sample-free item analysis. Educational and Psychological Measurement, 29, 23-48.

Theoretical prediction of test items. Burdick B, Stenner AJ. … Rasch Measurement Transactions, 1996, 10:1 p.475

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
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),
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
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
April 13-17, 2018, Fri.-Tues. AERA, New York, NY,
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