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

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 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
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
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), www.statistics.com
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, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
The HTML to add "Coming Rasch-related Events" to your webpage is:
<script type="text/javascript" src="http://www.rasch.org/events.txt"></script>

 

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

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