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-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
Rasch Books and Publications: Winsteps and Facets
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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	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
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

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