Whexact Wilson-Hilferty standardization = Yes
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-square 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
Example 2: A person takes a test of 20 dichotomous items and obtains an unweighted chi-square value of 19.5.
The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The exact normal deviate is .03, i.e., very slightly underfitting.
The OUTFIT mean-square is 0.975, i.e., apparently slightly overfitting. The reported normal deviate is -.08, i.e., slightly overfitting.
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|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
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|May 22 - 24, 2018, Tues.-Thur.||EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 27 - 29, 2018, Wed.-Fri.||Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org|
|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|July 25 - July 27, 2018, Wed.-Fri.||Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org|
|Aug. 10 - Sept. 7, 2018, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 12 - Nov. 9, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
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