Unidimensional Models in a Multidimensional World

Question: "Unidimensionality is one of the assumptions underlying most Rasch models. But everything we encounter is multidimensional. Why aren't all Rasch models multidimensional?"

Reply: The world is multidimensional and confusing. A fundamental activity of physical science is to decompose the world around us into unidimensional variables (weight, height, temperature, pressure, ...). Using these unidimensional variables, physicists can think clearly and make strong inferences. The history of the thermometer is an illustrative example of this process. Early thermometers (around 1600 A.D.) combined temperature with atmospheric pressure. They were "multidimensional". It was a major advance when scientists discovered how to separate those two dimensions in order to make both temperature and atmospheric pressure into unidimensional variables.

In Rasch measurement, we are attempting to perform the same process of splitting a multidimensional world into unidimensional variables, but now with social science. Asserting and then building unidimensional variables has been very useful in physical science. We expect it will also be in social science.


What if there are two dimensions?

Question: When we know there are two dimensions in the data, what is the next step - two separate analyses? Then, how can we make it sense out of the two analysis when we only want to report one number?

Answer: Under these circumstances, we need to consider:

1. How big is the difference between the dimensions?

2. How many people, and which people, does it impact?

3. Is it important enough to merit reporting two numbers?

This may require a separate analysis of each dimension. For instance, in an elementary-arithmetic test, we will probably find there is an "addition" dimension and a "subtraction" dimension. Unless the test is intended to identify learning difficulties, it is unlikely we will want to report two numbers. But the dimensionality may have useful information for instruction. In one situation, relatively bad performance on "subtraction" was discovered to be related to poverty. Children in poverty did not like the thought of something being "taken away" (subtracted). This suggests that teaching "subtraction" to impoverished children should avoid using emotive words or personal implications.

It is unusual in a carefully-constructed test that two dimensions are different enough inferentially to merit reporting two numbers. But secondary dimensions may indicate that care should be taken in test-construction in order to balance items between dimensions. For instance, aim for 50% addition items and 50% subtraction items, not 80% addition items and 20% subtraction items.



Linacre J.M. (2009) Unidimensional Models in a Multidimensional World, Rasch Measurement Transactions, 2009, 23:2, 1209



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

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. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt232d.htm

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