Fit to Models: Rasch Model vs. Correlation Model

Viewed as a statistical device, the Rasch model is one of thousands in current use. One of those thousands most frequently employed is the Pearson Correlation Model.

The Correlation Model

The size of the Pearson product-moment correlation between two variables is frequently reported, sometimes accompanied by whether it is significantly different from 0.00. But rarely reported are:

1) whether the observed correlation departs insignificantly from 1.00, which is perfect correlation. But high correlations, regardless of their statistical significance, could be indicative of collinearity. Near-perfect correlation should be regarded with suspicion.

2) whether the observations violate the assumptions underlying the Correlation Model. Violations are rarely tested explicitly because the correlation model is too useful not to use. Pearson correlations are often reported for data which are known not to meet its assumptions.

The Rasch Model

The Rasch model is similarly too useful not to use. Further, near perfect fit to the Rasch Model should be regarded with suspicion. Empirical processes are uneven. The validity of scientific work has come into question when statistical findings appear to be too perfect.

Taking the same position with regards to the Rasch Model as we do for the Correlation Model, the crucial question is not "Is the correlation statistically 1.0", expressed as "Do the data fit the Rasch model statistically perfectly?" This question has been the focal point of most global fit analysis with the Rasch model. Instead the crucial question becomes "Is the correlation statistically different from 0.00", expressed as "Is there a Rasch dimension which is significantly larger than a point?"

The Rasch dimension reduces to the size of a point when the data are perfectly random. Jacob Cohen (1992) suggests that, for the ratio of explained variance to unexplained variance, 2% is a small effect size, 15% is a medium effect size, and 35% is a large effect size. Recast this as the percentage of total variance explained and 2% is a small effect size, 13% is a medium effect size, and 26% is a large effect size. For comparison, the variance explained by the Rasch measures for the Liking for Science data is 51% [revised, 2008] and for the Knox Cube Test data is 71% [revised, 2008]. Even the variance explained for a relatively central, poorly fitting, NSF survey data set is 30% [revised, 2008]. Rasch papers can routinely report effect statistics, which, if they were the findings of correlation studies, would produce great joy among social scientists.

John M. Linacre

Cohen J. (1992) A Power Primer, Psychological Bulletin, 112, 155-159.

Fit to Models: Rasch Model vs. Correlation Model. Linacre J.M. … Rasch Measurement Transactions, 2005, 19:3 p. 1029

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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