Partial Credit model
The "Partial Credit" Rasch model was devised for multiple-choice questions in which credit is given for almost-correct distractors. But there is no reason to believe that the almost-correctness of distractors to different questions is the same. Consequently, each item is modeled to have its own response structure.
This model was extended to any questionnaire using ordered polytomies in which the response structure is modeled to be unique to each item.
Winsteps estimates response structures by item groupings, using ISGROUPS=. From this perspective, the Andrich Rating Scale Model includes all items in one grouping. The Masters Partial Credit Model allocates each item to its own grouping.
The conventional representation of the Partial Credit model is
log ( Pnij / Pni(j-1) ) = Bn - Dij
Winsteps parameterizes Dij as Di + Fij where sum(Fij) = 0. And Di is the average (Dij).
log ( Pnij / Pni(j-1) ) = Bn - Di -Fij
Algebraically these two representations are identical.
Thus every item has a mean difficulty, Di. This simplifies communication, because the results of a Partial Credit analysis now have the same form as any other polytomous analysis supported by Winsteps.
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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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|Coming Rasch-related Events|
|Jan. 5 - Feb. 2, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Jan. 10-16, 2018, Wed.-Tues.||In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement|
|Jan. 17-19, 2018, Wed.-Fri.||Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website|
|Jan. 22-24, 2018, Mon-Wed.||In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx|
|April 10-12, 2018, Tues.-Thurs.||Rasch Conference: IOMW, New York, NY, www.iomw.org|
|April 13-17, 2018, Fri.-Tues.||AERA, New York, NY, www.aera.net|
|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|
|Sept. 3 - 6, 2018, Mon.-Thurs.||IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org|
|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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