MESA Memo 48: Rasch model for Likert scales

SUMMARY EQUATIONS ON NOTES FOR A RASCH MODEL FOR LIKERT SCALES

Note: This paper contains the Andrich (1978) Rating Scale model, fully and independently developed.

David Andrich, 1977

MESA Research Memorandum Number 48
MESA PSYCHOMETRIC LABORATORY

This paper was presented at the
AERA Rasch Measurement Workshop
New York, 1977

Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Rasch Meta-Metres of Growth for Some Intelligence and Attainment Tests: A Meta-metre for some Intelligence and Attainment Tests, David Andrich, Ida Marais, Sonia Sappl

Rasch-Related Resources: Rasch Measurement YouTube Channel

Rasch Measurement Transactions & Rasch Measurement research papers - free

An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse

Rasch Measurement Theory Analysis in R, Wind, Hua

Applying the Rasch Model in Social Sciences Using R, Lamprianou

El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.

Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar

Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch

Rasch Models for Measurement, David Andrich

Constructing Measures, Mark Wilson

Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters

Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias

Diseño de Mejores Pruebas - free, Spanish Best Test Design

A Course in Rasch Measurement Theory, Andrich, Marais

Rasch Models in Health, Christensen, Kreiner, Mesba

Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

Rasch Books and Publications: Winsteps and Facets

Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene

Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver

Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone

Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale

Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland

Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes

Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang

Statistical Analyses for Language Testers (Facets), Rita Green

Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind

Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M

Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind

Rasch Measurement: Applications, Khine

Winsteps Tutorials - free
Facets Tutorials - free

Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre

Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

Rasch Meta-Metres of Growth for Some Intelligence and Attainment Tests: A Meta-metre for some Intelligence and Attainment Tests, David Andrich, Ida Marais, Sonia Sappl

Coming Rasch-related Events
Jan. 16 - Feb. 13, 2025, Fri.-Fri.	On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Apr. 8 - Apr. 11, 2026, Wed.-Sat.	National Council for Measurement in Education - Los Angeles, CA, ncme.org/events/2026-annual-meeting
Apr. 8 - Apr. 12, 2026, Wed.-Sun.	American Educational Research Association - Los Angeles, CA, www.aera.net/AERA2026
May. 15 - June 12, 2026, Fri.-Fri.	On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 19 - July 25, 2026, Fri.-Sat.	On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com