Psychometric Entities

Since Thales (6th century BC) first proposed substituting empirical ideas for spiritual explanation, rigid thinkers have attempted to restrict and control scientific thinking. For instance, consider the rule: "When theories and facts are in conflict, the theories must yield" (Simon, 1989). Perhaps this is true ultimately, but certainly not immediately. Such a rule could reduce science to merely summarizing the current empirical data, decrying as automatically invalid any theory that can be contradicted in any way by "hard facts".

The reoccurring attempt to impose dogma on empirical methods and its persistent rejection by scientists are summarized by Feyerabend below:
Not a single rule, .... however firmly grounded in epistemology, .... is not violated at some time or other .... atomism in antiquity, the Copernican Revolution, the rise of modern atomism (kinetic theory; dispersion theory; stereochemistry; quantum theory), and the gradual emergence of wave theory occurred only because some thinkers either decided not to be bound by certain "obvious" methodological rules, or because they unwittingly broke them. (Feyerabend, 1978, p. 230-231)

The best defense of scientific inference is a fundamental understanding of its empirical implications. This is as true of Rasch measurement as of any other theory. Michell claims that "no psychological attribute can ever be shown to be measurable" (2002). I concur with Graves (2003) in his emphasis that the more important issue is "how well these putative measurements .... relate to other behaviors and other theories" (p. 915). This more constructive approach to advancing social science aims at better understanding the influence of measurement on "psychometric knowledge", and specifically on psychometric and conceptual entities.

Conceptual entities are fictions or "working hypotheses" invented by scientists to explain dynamic regularities, and they are typically expressed as mathematical abstractions. When they lead to empirical predictions, both entities and abstractions acquire material status and become scientifically important. Molecular movement, for example, was mere speculation until the empirical demonstration of Brownian motion.

In psychometrics, researchers may fail to realize that entities offer conceptual foundations for addressing a whole host of scientific questions concerning meaningfulness and theory, many far more important than mere measurability criteria. For example, any group of items showing reasonable Rasch model fit can be claimed to exhibit not only empirical measurement properties, but also material status as a mathematical object. That is the point of calibrating items and measuring persons, because they provide empirical foundations for something "real" such as an ability or a psychological trait.

An item-person map represents an ability or psychological entity that was inferred by a mathematical abstraction and, when data fit, it reveals a reproducible aspect of experience. In this context, an item parameter value is not a transient sample artifact, but a quantitative object with exact and tangible material properties that are reaffirmed whenever item responses are analyzed. The material significance of this conceptual entity, now specifically a "psychometric entity", increases as framework invariance is verified and extended.

Physical theory provides many examples that reinforce the importance of conceptual entities for constructing scientific knowledge. In fact, the importance of conceptual entities in scientific theory is difficult to overstate (Maxwell, 1999). Electrons, gravity, and planetary orbits are material entities that are central to understanding a wide range of physical observations. (Prominent historical failures are phlogiston, aether, and humors -- among many others.) While originally the conceptual entities had no reality or ontological status, but were only conjectures within physical theory, scientists have expressed them in mathematical abstractions and linked them to empirical "reality".

Using linear measuring instruments, their empirical implications have provided foundations for an enormously successful body of scientific knowledge, and scientific advances have led to mathematical consolidations such as the reduction of chemistry to physics. (Consider Newton's inverse square law which governs movement of both planets and electrons.) This achievement is remarkable because scientists have never "seen" an electron, gravity, or planetary orbits but only highly predictable empirical effects.

In contrast, the ontological status of psychometric entities in education and psychology are scientifically eccentric because raw score rank order reliability and correlation are virtually their only claim to material status which, not surprisingly, has severely inhibited their maturation as scientific disciplines. Raw score structures provide only fleeting glimpses of a reality that is dependent on particular item sets and samples. A logical consequence is fragmented and discontinuous constructs that are virtually impossible to consolidate or integrate into an overall body of scientific propositions. The mathematical object offered by Rasch measurement preserves the rank-order achievements of 20th century psychometrics but offers much more. First it reveals meaningfulness that is inherent in a transitive numerical item structure (probabilistic additivity insures axiomatic transitivity). Second, it presents a common quantitative framework which facilitates consolidation of disparate data sets. The ontological significance of this framework gains scientific importance as measures with an explicit metric are related to other variables in mathematical functions - not just rank-order correlations. When mathematical functions are subsumed under comprehensive explanatory theories, they demonstrate science's explicit intention to reduce and unify knowledge. While ontology and entities may seem obscure and irrelevant to researchers and practitioners, in fact, they determine the "kind" of science that we practice. Psychometric entities with additive, linear measurement properties profoundly improve what we "know" from test scores. They open a window on scientific knowledge which is certainly more important than preoccupations about measurability. In the contemporary psychometric climate, a coherent understanding of why we should do more than simply compute test score reliability is an unusual opportunity to advance social science.
Nikolaus Bezruczko

Cohen, B. I. (1985) Revolution in Science. Cambridge, Massachusetts.: Harvard University Press.
Feyerabend, P. (1978). Against method. London: Verso.
Graves, R. E. (2003). In pursuit of Rasch measurement: Explorations following Michell. RMT, 17, 1, 914-915.
Maxwell, G. (1999). Theoretical entities. In Robert Klee (Ed.) Scientific Inquiry: Readings in the Philosophy of Science. Oxford: Oxford University Press.
Michell, J. (2002). Conjoint measurement and the Rasch model: Quantitative versus ordinal structure. Paper at IOMW, New Orleans, 2002.
Simon, H. (1989) Remark in W. Sichel (Ed.) The State of Economic Science. Upjohn.

Psychometric entitites. N. Bezruczko… 17:2 p. 922-923.

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

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