Whexact Wilson-Hilferty standardization = Yes

This is for 32-bit Facets 3.87. Here is Help for 64-bit Facets 4

Some versions of Facets are restricted to WHEXACT=NO.

 

ZSTD INFIT is the "Standardized Weighted Mean Square" shown at the bottom of RSA p. 100.

ZSTD OUTFIT is the "Standardized Unweighted Mean Square" based on the terms on RSA p. 100.

The Wilson-Hilferty transformation converts mean-square values to their equivalent "standardized" normal deviates. See RSA p. 101 and www.rasch.org/rmt/rmt162g.htm

In Facets, the chi-squared degrees of freedom (2/qi^2) are allowed to be less than 1.0.

 

Under certain circumstances, Wilson-Hilferty can correctly report the paradoxical finding that the mean-squares indicate overfit, but the normal deviate indicates underfit. To allow this possibility, specify WHEXACT=Y. To suppress it, specify WHEXACT=N. The final q/3 term is omitted from the transformation.

 

With WHEXACT= Yes, notice that the left side of this plot is non-centered vertically:

 

Example 1: You have obviously contradictory mean-square and standardized fit statistics. The mean-square is much less than 1, indicating considerable overfit, but the Zstd is much more than 0, indicating significant underfit. Here the Wilson-Hilferty approximation has failed. Specify WHEXACT=No

 

WHEXACT=Yes

WHEXACT=No

 

Example 2: A person takes a test of 20 dichotomous items and obtains an unweighted chi-squared value of 19.5.

 

WHEXACT=Y
The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The exact normal deviate is .03, i.e., very slightly underfitting.

 

WHEXACT=N
The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The reported normal deviate is -.08, i.e., slightly overfitting.


Help for Facets Rasch Measurement and Rasch Analysis Software: www.winsteps.com Author: John Michael Linacre.
 

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Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn, 2024 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
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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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