Rasch models: how to implement in Facets

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

Data =

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 http://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), http://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 http://www.rasch.org/rmt/rmt52j.htm

Example: completing a series of tasks

 

Models = ?,?,?,?, D

Labels =

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 http://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 http://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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Rasch Publications
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
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

 

Coming Winsteps & Facets Events
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
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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