Rasch family of two-facet measurement models

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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


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