Robustness and Invariance

Statistical notions of robustness are disappointingly distant from the essential criteria and procedures of invariance. So claims philosopher of science, William Wimsatt (1981). Wimsatt identifies four criteria that must be negotiated before the resulting determination can be labeled "robust". These require the researcher:

1) to analyze the problem through a variety of independent derivation, identification or measurement processes.

Rasch: Every interaction between elements (persons, items etc) entering into a measurement analysis adds to the variety of independent processes.

2) to look for and analyze things which are invariant over or identical in the conclusions or results of these processes.

Rasch: Instruments are developed and measures are obtained by looking for and analyzing what is invariant over the qualitative responses which are outcomes of element interactions.

3) to determine the scope of the processes across which the things are invariant and the conditions on which their invariance depends.

Rasch: The construction of a variable requires construct validity and an understanding of the meaning and useful range of the constructed variable, e.g., "arithmetic competence" and its associated "high" and "low" ability students, and "easy" and "hard" difficulty items.

4) to analyze and explain any relevant failures of invariance.

Rasch: Investigation of misfitting responses leads to respecification of the problem, elimination of defective data, or the determination that the threat to invariance is inconsequential.

Thus Rasch analysis satisfies these criteria and so, according to Wimsatt, produces "robust" determinations.

Wimsatt also makes observations about the consequences of robustness:

1) Misfit "can provide an almost magical opportunity for discovery."

Rasch: Intriguing new variables are discovered when responses systematically misfit their intended variables.

2) "Only robust hypotheses are testable."

Rasch: Hypotheses based on Rasch measures are as independent as possible of data vagaries. Hypotheses based on descriptive statistical techniques, like regression, are at the mercy of arbitrary parameterizations and errant observations. Such hypotheses are untestable because their bases are unreproducible.

3) "Robustness helps distinguish signal from noise."

Rasch: The measurement model identifies what constitutes signal (the variable) and what constitutes noise (the error). During analysis, noise is separated from signal. Average noise level is the frame of reference for determining signal strength. Noise unevenness causes signal distortion (misfit).

Rasch's awe-inspiring insight was that a certain level of "failure of invariance", i.e., noise, is essential if the variable, i.e., signal, is to be measured.

William P. Fisher, Jr.

Wimsatt, William C. 1981. Robustness, reliability, and overdetermination. p. 124-163 in M.B. Brewer & B.E. Collins (Eds) Scientific Inquiry and the Social Sciences. San Francisco: Jossey Bass.

Robustness and invariance. Fisher WP Jr. … 1993, 7:2 p.295

Robustness and invariance. Fisher WP Jr. … Rasch Measurement Transactions, 1993, 1993, 7:2 p.295

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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