# My Best Items Don't Fit!

"I have a instrument of 13 items. I used the Partial Credit model. There are 3 items whose INFIT "t" statistic (ZSTD) is outside -9.9, and so significantly misfitting my Rasch model. But these items' score correlations are greater than 0.83. The discrimination of these three items' is higher than the other 10 items, so in classical test theory (CTT) and much of IRT, these are my best three items. Should I say that the Rasch model is not suitable for this instrument, and maybe a Generalized (2-parameter) Partial Credit model analysis is indicated?

Desperate Test Constructor

t-statistics (ZSTD) are tests of the hypothesis "these data fit the model perfectly." In statistics this is called a "false null hypothesis", because it can never be true! No empirical data fit the Rasch model perfectly. So a more crucial question is, "Do the data fit the model usefully?" "Do they distort the measures more than they contribute to measurement accuracy and precision?"

Here are some steps to take in your investigation:

1. Those three items are over-discriminating from a Rasch perspective. Are these items really good items or are they substantively flawed? Look at the content of the items and refer to Geoff Masters (1988) "Item discrimination: when more is worse", Journal of Educational Measurement, 25:1, 15-29, and www.rasch.org/rmt/rmt72f.htm - RMT 7:2, 289.

2. Don't be intimidated by the statistics. What is your sample size? Is it making the hypothesis test too sensitive? See www.rasch.org/rmt/rmt171n.htm - RMT 17:1, p. 918. Are the mean-squares (chi-squares divided by their degrees of freedom) so close to their expectations that the differences have no substantive implications, despite being significantly unexpected?

3. Are the three items contributing to accurate measurement, or are they distorting measurement? The usual way to check this is to measure the persons with and without these 3 suspect items and cross-plot the person measures. Who is off the diagonal? Which set of measures better represent the abilities of your sample?

4. If these 3 items really are substantively "bad", changing the analytical model will not make them "good". A different model will merely hide the symptoms. So omitting the items is preferable to changing the analytical model.

My best items don't fit!, … Rasch Measurement Transactions, 2004, 18:3 p. 992

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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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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
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Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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