Rasch models: how to implement in Facets |
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Facets can estimate all commonly-used Rasch unidimensional models, and many less familiar ones.
1. Rasch dichotomous model (usually equivalent to 1-PL model).
Example: True-false test. Multiple-choice test
Models = ?,?,?,D
1, 2, 3, 0 ; for failure
1, 2, 3, 1 ; for success
2. Andrich rating-scale (restricted) model
Example: survey using Likert scale
Models = ?,?,?,Rn ; where n is highest category of the rating scale
Data =
1, 2, 3, 1 ; for strongly disagree
1, 2, 3, 2 ; for disagree
1, 2, 3, 3 ; for neutral
1, 2, 3, 4 ; for agree
1, 2, 3, 5 ; for disagree
3. Masters partial-credit (unrestricted) model
Example: Multiple-choice test with distractors scored by knowledge level.
Models = ?,?,#,Rn ; where n is highest category of the partial-credit scale
Data =
1, 2, 3, 0 ; for wrong
1, 2, 3, 1 ; for partially correct
1, 2, 3, 2 ; for correct
4. Bernoulli binomial-trials model (with item discrimination), see https://www.rasch.org/rmt/rmt132a.htm
Example: hits on a target
Models = ?,?,?,Bn ; where n is the number of trials (attempts)
Data =
1, 2, 3, 0 ; no successes
1, 2, 3, 1 ; one success
1, 2, 3, 2 ; two successes
5. Poisson-counts model (with item discrimination), https://www.rasch.org/rmt/rmt132a.htm
Example: spelling mistakes in a long dictation test
Models = ?,?,?,P ; where the maximum count is conceptually infinite and
; maximum observable successes = 255
Data =
1, 2, 3, 0 ; no successes
1, 2, 3, 1 ; one success
1, 2, 3, 2 ; two successes
6. Glas "Steps" success model, see https://www.rasch.org/rmt/rmt52j.htm
Example: completing a series of tasks
Models = ?,?,?,?, D
3 = Items facet, A
6 = Item 6 element, 0 ; anchored at 0 to give item fit statistics,
; for interactions, etc.
*
4 = Decision point facet
61 = first step element for item 6
62 = second step for item 6
*
Data =
; first step of task failure
1, 2, 6, 61, 0 ; failure on item 6 step 1
1, 2, 6, 62, . ; item 6 step 2 not attempted
; first step of task success, second step failure
1, 2, 7, 71, 1 ; success on item 7 step 1
1, 2, 7, 72, 0 ; failure on item 7 step 2
; first step of task success, second step success
1, 2, 8, 81, 1 ; success on item 8 step 1
1, 2, 8, 82, 1 ; success on item 8 step 2
7. Rasch failure model, see https://www.rasch.org/rmt/rmt52j.htm
Example: performing a task within time-limits
Models = ?,?,?,?, D
Labels =
3 = Item facet, A
6 = Item 6 element, 0 ; anchored at 0 to give item fit statistics, for interactions, etc.
*
4 = Decision point facet
62 = second step for item 6: task performed immediately
61 = first step for item 6 element: task performed later
*
Data =
; task performed immediately = 2 points
1, 2, 6, 62, 1 ; success on item 6 step 2
1, 2, 6, 61, . ; item 6 step 2 not attempted
; task performed later = 1 point
1, 2, 7, 72, 0 ; failure on item 7 step 2
1, 2, 7, 71, 1 ; success on item 7 step 1
; task never done = 0 points
1, 2, 8, 81, 0 ; failure on item 8 step 1
1, 2, 8, 82, 0 ; failure on item 8 step 1
8. Rasch fractional dichotomous model, see https://www.rasch.org/rmt/rmt233d.htm
Example: percentages: performance assessed as 70% success on an item
Models = ?,?,?,D
Data =
; the data points are weighted using R, data replication.
R0.70, 1, 2, 3, 1 ; for 70% empirically-observed rate of success
; = 0.7 of a dichotomous success
R0.30, 1, 2, 3, 0 ; for 30% empirically-observed rate of failure
; = 0.3 of a dichotomous failure
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