Global Rasch Fit Statistic

Global Rasch Fit Statistic

Question: A Journal Editor insists I include a global statistic for fit of the Rasch model to my data. What do you recommend?

Answer: The Editor misunderstands the Rasch model, but this is not the moment to rectify that. Numerous global fit tests have been proposed reflecting the different ways in which the data can misfit the unattainable ideal of the Rasch model. Here's a practical approach. For each observation, there is a standardized residual and a model probability. So we can always compute usefully approximate chi-square statistics, regardless of missing data:

1. Pearson chi-square = sum of squared standardized residuals for all observations.

2. Log-likelihood chi-square = -2 * sum of the natural logarithms of the model probabilities for all observations. In practice, these values will differ. So we can choose the value better fitting our intentions, as is usually done in statistical modeling, or report both statistics. In both cases, the degrees of freedom for dichotomous data approximate:

d.f. = data point count - (person count + item count)

Omit items and persons with zero or perfect scores before doing these computations. For polytomies, also deduct from the d.f. the number of active categories (less 2) for each polytomous scale.

Since the expectation of a chi-square statistic is its d.f., you can obtain a more accurate estimate of the d.f. by simulating multiple sets of data with the same measurement structure as your data, and then using the average of their chi-square values as the reported d.f. for your chi-square.


Global Rasch Fit Statistic … Rasch Measurement Transactions, 2007, 21:2 p. 1103



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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