## Investigating Empirical ICCs

Engberg, Garde and Kreiner (EGK, 1995) investigate the measurement properties of the EG Motor Index for assessing patients mobility after a stroke. They discover that a 10 item observational instrument "can, at least to a certain extent, be regarded as unidimensional.., compatible with the concepts of regularity in recovery after stroke." Items include "Sitting balance", "Move sidewards supine" and "Sit up with legs over bed on sound side", rated 0=Totally unable, 1=With help, 2=Independent.

EGK do not report measures for their 180 patient assessments, nor calibrations for their 10 items. But they do report the empirical item characteristic curves [see Figure 1]. These are hard to evaluate by eye, though they do seem to have the expected ogival form.

Straight lines are easier to evaluate than curves. Figure 2 recasts the empirical values into logits which are expected to approximate linearity. The "% Probability" shown in Figure 1 is linearized by taking its logit: loge(%/(100-%)), substituting 0.5% for 0.0% and 99.5% for 100%. The raw score in Figure 1 (which substitutes for the person measure) is linearized by taking its logit: loge(score/(20-score)) where 20 is the maximum raw score. Figure 2 is clearer than Figure 1, but still confusing to the eye. The zig-zag form of each line provides an uninterpretable excess of detail that may merely reflect expected stochasticity in the data.

Figure 3 simplifies Figure 2 by replacing each zig-zag line with a single straight line that approximates it. If the data fit the Rasch model, the lines would be roughly parallel. In fact, the straight lines are almost parallel. Interesting deviations, such as that of item 8, can now be identified for further examination. Item 8, "Walking" is a much more athletic activity than the others listed, and so it more strongly differentiates different levels of mobility. Its steeper line signals higher discrimination. If EGK had reported local fit statistics, Item 8 would exhibit a muted INFIT mean- square, i.e., less than 1.0. This Figure also provides item calibrations at the ICC intercepts with the X-axis.

As William Fisher remarked (RMT 9:2 p. 426), perhaps their successful application of Rasch to this data will encourage EGK to use the results of their Rasch analysis to further aid in the construction of a yet more effective measuring instrument.

Engberg A, Garde B, Kreiner S (1995) Rasch analysis in the development of a rating scale for assessment of mobility after stroke. Acta Neurologica Scandinavica 91: 118-127.

Mobility after stroke: investigating empirical ICCs. Engberg A, Garde B, Kreiner S. … Rasch Measurement Transactions, 1995, 9:3 p.449

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: 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 31, 2017, Fri. Conference: 11th UK Rasch Day, Warwick, UK, www.rasch.org.uk
April 2-3, 2017, Sun.-Mon. Conference: Validity Evidence for Measurement in Mathematics Education (V-M2Ed), San Antonio, TX, Information
April 26-30, 2017, Wed.-Sun. NCME, San Antonio, TX, www.ncme.org - April 29: Ben Wright book
April 27 - May 1, 2017, Thur.-Mon. AERA, San Antonio, TX, www.aera.net
May 26 - June 23, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 30 - July 29, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
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
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