Quantifying Item Dependency

Some items are more closely related than others. Comprehension items that address the same written text and arithmetic items requiring the same operation are examples. In Rasch analysis, this is no major source for concern provided there is no extreme systematic dependency between two or a few items. When such dependency does exist, combining the separate items into one partial-credit item may be useful. Low values of the Rasch INFIT statistic signal dependency. When a diagnostically specific investigation of inter-item dependency is required, Fisher's Z is useful.

1)Obtain the Rasch-based standardized residuals for each observation of Person n on item i:

zni = (Observedni - Expectedni)/Standard Errorni

2)Correlate the standardized residuals for all pairs of items i, j across all N persons:

rij = (sum(zni znj) - sum(zni)sum(znj)/N) / N SD(zni) SD(znj)

3)Use Fisher's Z to linearize Pearson correlations:

Zij = 1/2 Loge( (1+rij)/(1-rij) )

4)Draw a histogram of the Fisher Z values. Noticeable positive skew (see Figures) indicates the presence of sets of dependent items. A cluster analysis of the Z matrix will identify the sets. Outlying positive Z values flag pairs or sets of highly dependent items for further investigation.

Fisher's z for dependent items


Fisher's z for independent items



Quantifying item dependency. Shen L. … Rasch Measurement Transactions, 1996, 10:1 p.485



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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