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Observed Ordinal Step Measurement Model
Type of Data: Categories/Interpretation/Score/for Loge[Pnij/Pnij-1]
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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
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More complex models decompose into these models.
Rasch family of two-facet measurement models, B Wright … Rasch Measurement Transactions, 1992, 6:2 p. 226
Please help with Standard Dataset 4: Andrich Rating Scale Model
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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: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. | Statistical Analyses for Language Testers, Rita Green |
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