Rasch family of two-facet measurement models

------------------------------------------------------------------
             Observed    Ordinal       Step  Measurement Model
Type of Data: Categories/Interpretation/Score/for Loge[Pnij/Pnij-1]
------------------------------------------------------------------
BASIC                no / less / 0 / Bn-Di
-Rasch               yes / more / 1 / j=1
COUNTS               0 / 0 / 0 / Bn-Di-Fi*loge[j]
-Rasch               infinity / inf / inf / j=1,inf
TRIALS               0 / 0 / 0 / Bn-Di-Fi*loge[j/(mi-j+1)]
-Choppin             mi / mi / mi / j=1,mi
RATINGS              1 / least / 0 / Bn-Di-Fj
-Andrich             2 / .  / 1 / .
                     m+1 / most / m / j=1,m
GRADES               A / highest / mi / Bn-Di-Fij
-Masters             B / . / mi-1 / .
 partial credit      Z / lowest / 0 / j=1,mi
RANKS                1 / first / mi / Bn-Fj  (complete)
-Linacre             2 / . / mi-1 / Bn-Fij  (partial)
                     mi / . / 1 / .
                     mi+1 / last / 0 / j=1,mi
PAIRED COMPARISON    0 / less / 0 / Bn-Bi  (forced choice)
-Bradley/Terry       1 / tie / 1 / Bn-Bi-Fj  (with ties)
                     2 / more / 2 / j=1,2
CREDITS              0 / 1st "item" wrong / 0 / Bn-Di-Fij
-Glas                1 / 2nd "item" wrong / 10 / .
 success             . / ... / 11.. / .
                     mi-1 / mth "item" wrong / 11..10 / .
                     mi / mth "item" right / 11..11 / j=1,mi
DEBITS               mi / mth "item" right / 1 / Bn-Di-Fij
 failure             mi-1 / m-1th "item" right / 10 / .
                     . / ... / ..00 / .
                     1 / 1st "item" right / 10..00 / .
                     0 / 1st "item" wrong / 00..00 / j=1,mi
NEARNESS             0 / before / 0 / Bn-Di-Fj
-Coombs              1 / here or now / 1 / .
-Andrich             0 / after / 2 / j=1,2
------------------------------------------------------------------

More complex models decompose into these models.


Rasch family of two-facet measurement models, B Wright … Rasch Measurement Transactions, 1992, 6:2 p. 226



Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. 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
Facets Tutorials - free		 Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other 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

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