Progress in Measurement Theory

We must explain why science - our surest example of sound knowledge - progresses as it does, and we first must find out how, in fact, it does progress.
Thomas Kuhn, 1970a, p.20

The adequacy or effectiveness of individual theories is a function of how many significant empirical problems they solve, and how many important anomalies and conceptual problems they generate.
Larry Laudan, 1977, p.119

How should "progress" be defined and evaluated for measurement theory? Progress can be defined in different ways. Bury (1932) provides a historical analysis of how the idea of progress has changed over time. This change continues. For some philosophers of science, progress is defined in terms of the number of empirical problems successfully solved (Kuhn, 1970b). Empirical problems are substantive questions about objects which constitute the domain of any given science (Laudan, p.15).

Other philosophers argue that the overall problem-solving effectiveness of a theory is determined by assessing the number and importance of empirical problems which the theory solves and deducting therefrom the number and importance of the anomalies and conceptual problems which the theory generates (Laudan, p.68). Conceptual problems are characteristics of theories with no existence independent of the theories themselves. Conceptual problems depend on the well-foundedness of the conceptual structures (e.g., theories) which have been devised to answer the first-order [empirical] questions (Laudan, p.48). Since conceptual problems could devalue even the most effective solution to an empirical problem, surely our definition of progress must encompass both components.

What are the major empirical and conceptual measurement problems in the social sciences? Are some problems more important than others? What are the criteria for defining acceptable solutions to crucial problems? Can objective criteria be developed for comparing the problem-solving effectiveness of different measurement theories?

In item response theory, IRT, the responses of individuals to test items define the objects of study. Empirical questions can be raised such as "How well does the model fit the data?" or "How well do data fit the model?" If empirical criteria alone defined problem-solving effectiveness, then the better theory would provide the better model-data fit. When, however, conceptual problems are also considered, theory evaluations must include the illogical consequences of some measurement theories, such as the crossed item characteristic curves that follow from Birnbaum's model, and the attenuation paradox of "true score" theory.

Once the crucial empirical and conceptual problems are defined, progress can be examined by comparing the problem-solving effectiveness of competing theories. The effectiveness of a single measurement theory can also be examined over time by evaluating how well it deals with new problems that did not exist when it was formulated. Computerized adaptive testing (CAT) systems did not exist when Spearman laid the groundwork for "true score" theory, nor when Rasch developed his measurement theory. We now see that "true score" theory cannot provide a useful solution for CAT measurement problems. On the other hand, practical CAT systems have been developed using the Rasch model.

Professor George Engelhard, Jr.
Emory University
Division of Educational Studies

Bury J.B. 1932. The idea of progress: An inquiry into its growth and origin. New York: Dover.

Kuhn T. 1970a. Logic of discovery or psychology of research? In Lakatos and Musgrave, Criticism and the growth of knowledge. London: Cambridge University Press.

Kuhn T. 1970b. The structure of scientific revolutions. 2nd Edition, enlarged. Chicago: The University of Chicago Press.

Laudan L. 1977. Progress and its problems: Towards a theory of scientific growth. Berkeley, CA: University of California Press.

Progress in Measurement Theory. G. Engelhard, Jr. … Rasch Measurement Transactions, 1992, 6:1, 204

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

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