Rasch Measures and Unidimensionality

Rasch measures never lose their unidimensionality (nor their linearity for the additive form of the Rasch model). Those properties are forced by the Rasch model. But we can lose the connection between the Rasch measures and the intended unidimensional latent variable.

Example: we want to measure "arithmetic ability". 1,000 children take our arithmetic test. 500 children respond to the items carefully. 500 children guess at random.

If we Rasch-analyze the 500 careful children, then we will obtain ability measures and item difficulties on the intended unidimensional, linear "arithmetic" latent variable with good fit of the data to the Rasch measures.

If we Rasch-analyze the 500 guessing children, then we will obtain person measures and item difficulties on a unidimensional, linear "random guessing" latent variable with good fit of the data to the Rasch measures..

If we Rasch-analyze 500 careful children + 500 guessing children, then we will obtain "ability" measures and item difficulties on a unidimensional, linear "arithmetic + random guessing" latent variable with poor fit of the data to the Rasch measures.

We might say, but "arithmetic + random guessing" is not substantively unidimensional! We know that, but the Rasch model does not. It analyzes the data as though they are unidimensional, and then the fit statistics report how well the data match the mathematically unidimensional framework that the Rasch analysis has constructed.

John M. Linacre

Rasch Measures and Unidimensionality, J.M. Linacre. ... Rasch Measurement Transactions, 2011, 24:4, 1310

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 www.rasch.org
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 Rasch.org

www.rasch.org 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, www.rasch.org.

Coming Rasch-related Events
Oct. 6 - Nov. 3, 2023, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets), www.statistics.com
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) www.colpsic.org.co
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com


The URL of this page is www.rasch.org/rmt/rmt244f.htm

Website: www.rasch.org/rmt/contents.htm