The Problem of Measure Invariance

Ben Wright:
"If the difficulty of an item were not invariant over some useful domain, then the term difficulty would have no useful meaning. The inch on my wooden yardstick is invariant as long as I don't use the yardstick inside the furnace and, of course, am careful to (a) originate the zero end of the yardstick at the place from which I want to measure a difference and (b) align the yardstick parallel to the direction in which I want to measure and (c) hold the yardstick still and (d) look carefully, with my glasses on, to see as sharply as I can what inch mark seems to be reached. And, when I am serious, I will replicate this procedure several times first to exclude wild values and finally to extract one value with an allowance for error which I will then use as the measure."

M. Hubey:
"I think something will have to be done with this concept that takes into account the fact that the brain/mind is not like anything else. If the maximum weight I can lift with my single arm is 70 lbs, it will also be the same the next day, and the day after etc. It will take a long time before lifting that weight becomes easier. But with problem-solving techniques it is instantaneous. If I learn how to solve a particular kind of problem, no matter what its degree of difficulty, it is a done-deal. Next time it is no longer difficult."

Tom O'Neill:
"It seems that the person merely has more ability after learning the new problem-solving technique. Having learned the technique does not change the difficulty of that type of problem relative to the other problems. If, however, there is no hierarchy of problems and problem solving techniques are not acquired in any particular order, then measurement is not possible. For example, if you can perform long division, I assume that you can also do single digit addition. This is because I envision a hierarchy of math operations. When you violate this common understanding of math ability, common because when calibrating various problems they maintain the same relative difficulty, I must decide what to do with your improbable response. Were you careless on the single digit addition? Were you lucky on the long division? Does your math ability conform to the common understanding of math ability?"

John Michael Linacre:
"In fact, the loss of invariance is major challenge to pre-post test equating. If I can't read Chinese, at the pre-test, all sentences in Chinese are equally difficult to read. When I can read some Chinese, at the post-test, some sentences are easy and some are hard. When I'm learning to drive a car, some things are easy and some things are hard. When I've learned to drive, all essential skills are equally easy. So where is the yardstick? We have to decide which situation corresponds to our intention to measure, and then use that situation to quantify the invariant measures that we will apply everywhere. The metrologists follow exactly this procedure when they construct physical measuring instruments."

The Problem of Measure Invariance. Wright, B.D., Huber, M., O'Neill, T., Linacre, J.M. … Rasch Measurement Transactions, 2000, 14:2 p.745

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	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
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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
Other 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

Forum

Rasch 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.

The URL of this page is www.rasch.org/rmt/rmt142d.htm

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