Mixed rating scale (partial credit) forms and MCQ scoring keys

Facets handles mixtures of rating scales and partial credit items within the same test easily using Models=.  Datasets containing only MCQ items can be analyzed.


Items 1-10 are dichotomies, already scored 0,1

Items 11-14 are 3-category rating scales 1,2,3 - each with its own scale definition, i.e., partial credit items.

Items 15 is a binomial count 0-10 successes


Facet 1 is person, Facet 2 is judge (only for items 11-14), Facet 3 is item:



?, X, 1-10, D  ; items 1-10 -dichotomies - no judge

?, ?, 11-14#,R3 ; items 11-14 - each with own scale

?, X, 15, B10 ; item 15 - 10 binomial trials



Here are typical lines of data for person 23:


23,0,1-10,0,1,1,1,1,0,0,0,1,1 ; person 23, with no judge, responds to items 1-10, scored 0 or 1.

23,3,11-14,3,2,3,1  ; person 23, judge 3, rated on items 11-14 on rating scales with highest category 3.

23,6,12-14,1,,3   ; person 23, judge 6, rates only items 12 and 14

23,0,15,7   ; person 23, no judge, 7 successes out of 10 binomial trials.


To score multiple-choice MCQ dichotomies:


The scoring key for the 10 items is: CADBDCDABB


Also shown are items 11-14 which are partial credit or rating scale items.

Item 15 is a binomial trial item giving successes out of 10.



?,X,1,C  ; using scoring key C as the model code










?, ?, 11-14#,R3 ; items 11-14 - each with own scale

?, X, 15, B10 ; item 15 - 10 binomial trials


Rating (or partial credit) scale=A,D ; Scale A - dichotomous

0=Wrong,,,B+C+D+ ; add other possible wrong responses here

1=Right,,,A  ; ",,," is to skip over anchor value positions


Rating (or partial credit) scale=B,D

0=Wrong,,,A+C+D+.    ; add other possible wrong responses here



Rating (or partial credit) scale=C,D

0=Wrong,,,A+B+D+.    ; add other possible wrong responses here



Rating (or partial credit) scale=D,D

0=Wrong,,,A+B+C+.    ; add other possible wrong responses here



; Here are typical lines of data for person 23:


23,0,1-10,D,B,C,A,.,D,A,B,D,C ; person 23, with no judge, responds to items 1-10

23,3,11-14,3,2,3,1  ; person 23, judge 3, rated on items 11-14

23,6,12-14,1,,3   ; person 23, judge 6, rates only items 12 and 14

23,0,15,7   ; person 23, no judge, 7 successes out of 15.

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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
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Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
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