With any set of polytomous items, where all response categories are logically possible for each item, it will sometimes happen that certain categories are unused in the immediate sample of data. This sample characteristic can not be allowed to interfere with a response framework which is a characteristic of the research design. The distinction between a logically null category and a category that is observed to be null in some sample is analogous to the distinction between a structural zero and a sampling zero in contingency table analysis (Fienberg 1985). When a category is not used for a particular item, we would not recommend omitting reference to that category by down-coding the categories above it, such as is the default in many Rasch analysis programs. This kind of down-coding can alter a person's ranking on a test. Of course, when a sampling zero occurs repeatedly for a particular item, it is wise to examine the item for an explanation.
A simple modification of the Partial Credit model retains all categories so that none are "collapsed" out (Wilson & Masters 1991). This reformulation has been incorporated into several Rasch programs. The partial-credit scale has categories 0 to mi. If z is the category corresponding to a sampling zero (with local probability of zero) and categories z-1 and z+1 are present in the data, then, in the notation of Wright & Masters (1982),
Pnix = exp(sum j=0 to x (except z) (Bn - Dij) /
sum k=0 to mi (except z) (exp (sum j=0 to k (except z) ((Bn - Dij) )
with Pniz locally zero.
The full set of Andrich thresholds can be approximated by:
D' = Diz-1, iz+1 skipping over Diz
Di1, Di2, ..., Diz-1, Diz=D'+40, Diz+1=D'-40, ... Dmi
then Pniz ≈ 0
Example: if a dichotomous 0,1 observation is recoded as a polytomous 0,(1),2 observation, where 1 is unobserved, then
For 0-1 the Andrich threshold is 0 relative to the item difficulty.
For 0-(1)-2 the Andrich thresholds are 40, -40 relative to the same item difficulty.
See also: Unobserved categories: Estimating and anchoring Rasch Measures. RMT 17:2 p. 924-925
Rasch Estimation with Unobserved or Null Intermediate Categories, M Wilson Rasch Measurement Transactions, 1991, 5:1 p. 128
|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|
|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|
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement
Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.
|Coming Rasch-related Events|
|Sept. 27-29, 2017, Wed.-Fri.||In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement|
|Oct. 13 - Nov. 10, 2017, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Oct. 25-27, 2017, Wed.-Fri.||In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement|
|Dec. 6-8, 2017, Wed.-Fri.||In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement|
|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|
|Jan. 17-19, 2018, Wed.-Fri.||Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website|
|April 13-17, 2018, Fri.-Tues.||AERA, New York, NY, www.aera.net|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|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|
The URL of this page is www.rasch.org/rmt/rmt51b.htm