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 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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