Louis Guttman conceptualized an ideal scale with the property that knowledge of only the number of items a respondent passes tells the researcher exactly which items the respondent passes. Guttman (1947, 1950) does this by constructing a "scalogram" of the scored responses, in which each column corresponds to a respondent, arranged left to right in decreasing raw score order, and each row corresponds to an item, arranged top to bottom in decreasing order of respondent success. The item on which the respondents are the most successful comes first. When Guttman's ideal is realized, the responses in the top left of the scalogram are all successes and in the bottom right are all failures. There is a distinct diagonal demarcation between success and failure, with no disordering or "inversion" of successes and failures.
In practice, of course, Guttman's ideal is unobtainable, as he well knew. Accordingly he established rules which position a "cutting line" for each respondent at that place in the string of responses which minimizes the number of inversions for that respondent. This is a kind of "least error" fitting of a deterministic ideal to uncertain data. Unfortunately Guttman's rule leads to ambiguous results. If the responses are 1010 to the items ordered in ascending order of difficulty, both 1!010 and 101!0 are "least inversions" placements of the cutting line for one inversion. This has not gone unnoticed and procedures for dealing with this problem have been proposed.
Kenny and Rubin (1977) object to the ambiguity, arbitrariness and lack of clear theoretical basis which underlie the attempts to solve this problem. They build on Guttman's concept of "reproducibility", the proportion of scalable, correctly placed responses in the data. Guttman minimized the inversions one respondent at a time, with ambiguous results. Kenny and Rubin assert that the inversions are more meaningfully reduced by considering all respondents with the same raw score together. This yields the unambiguous result that the cutting line is placed at that point where the observed number of successes would be were the data perfectly scalable. All respondents with the same raw score get the same cutting line, regardless of the number of inversions within each pattern of responses. This is the default in the scalogram programs, SAS and SPSS-X.
The default is well chosen. Ordering by raw score is identical to requiring that raw score be a sufficient statistic. But this requirement leads directly to the Rasch model as the only explanation for the data. Guttman reproducibility, constrained by unambiguity, is equivalent to the Rasch model.
Guttman L 1947. The Cornell technique for scale and intensity analysis. Educational and Psychological Measurement, 7, 274-279
Guttman L 1950. The basis for scalogram analysis. In Stouffer et al. Measurement and Prediction. The American Soldier Vol. IV. New York: Wiley
Kenny DA, Rubin DC 1977. Estimating chance reproducibility in Guttman scaling. Social Science Research, 6, 188-196.
Stochastic Guttman order. Linacre JM. Rasch Measurement Transactions, 1992, 5:4 p.189
|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|
|March 21, 2019, Thur.||13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019|
|April 4 - 8, 2019, Thur.-Mon.||NCME annual meeting, Toronto, Canada,https://ncme.connectedcommunity.org/meetings/annual|
|April 5 - 9, 2019, Fri.-Tue.||AERA annual meeting, Toronto, Canada,www.aera.net/Events-Meetings/Annual-Meeting|
|April 12, 2019, Fri.||On-line course: Understanding Rasch Measurement Theory - Master's Level (G. Masters), https://www.acer.org/au/professional-learning/postgraduate/rasch|
|July 2-5, 2019, Tue.-Fri.||2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org|
|July 11-12 & 15-19, 2019, Thu.-Fri.||A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses|
|Aug 5 - 10, 2019, Mon.-Sat.||6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html|
|Aug. 9 - Sept. 6, 2019, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Aug. 14 - 16, 2019. Wed.-Fri.||An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs|
|August 25-30, 2019, Sun.-Fri.||Pacific Rim Objective Measurement Society (PROMS) 2019, Surabaya, Indonesia https://proms.promsociety.org/2019/|
|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt54p.htm