Trials with Vertical Equating

I ran into some problems with vertical equating. My bank contains 1,000 items from beginner level to very advanced. What I found was that the spread of difficulties calculated for any one test form was too wide. Extremely high or low percentage-correct scores produced ability and item difficulty estimates that were too far from the test form mean. This meant that, when test forms were combined, the most difficult, but still easy, items in a dead easy test form came out at an intermediate level when all the forms were linked into the bank. The same problem occurs for person abilities. My solution has been to cut off the top and bottom 20% of raw scores. This, combined with excluding or retrialling items that were badly targeted first time round, considerably reduced the apparent logit range of item difficulties, and produced an item difficulty line-up that makes sense.

Ben Wright comments:
The Rasch model provides measures for items relevant to persons. Off- target items provoke guessing, carelessness and other misbehaviors that reduce the measurement capabilities of the test. Neil's sensible solution to this problem is motivated by a fundamental concern: results have got to make sense! No statistical sleight of hand is going to do better than Neil has done. Neil, have you tried building your bank with just one global calibration (one-step (concurrent) vertical equating)?

Trials with Vertical Equating, N Jones & B Wright … Rasch Measurement Transactions, 1992, 6:3 p. 240

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
Oct. 6 - Nov. 3, 2023, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets),
Oct. 12, 2023, Thursday 5 to 7 pm Colombian timeOn-line workshop: Deconstruyendo el concepto de validez y Discusiones sobre estimaciones de confiabilidad SICAPSI (J. Escobar, C.Pardo)
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),


The URL of this page is