# My Best Items Don't Fit!

"I have a instrument of 13 items. I used the Partial Credit model. There are 3 items whose INFIT "t" statistic (ZSTD) is outside -9.9, and so significantly misfitting my Rasch model. But these items' score correlations are greater than 0.83. The discrimination of these three items' is higher than the other 10 items, so in classical test theory (CTT) and much of IRT, these are my best three items. Should I say that the Rasch model is not suitable for this instrument, and maybe a Generalized (2-parameter) Partial Credit model analysis is indicated?

Desperate Test Constructor

t-statistics (ZSTD) are tests of the hypothesis "these data fit the model perfectly." In statistics this is called a "false null hypothesis", because it can never be true! No empirical data fit the Rasch model perfectly. So a more crucial question is, "Do the data fit the model usefully?" "Do they distort the measures more than they contribute to measurement accuracy and precision?"

Here are some steps to take in your investigation:

1. Those three items are over-discriminating from a Rasch perspective. Are these items really good items or are they substantively flawed? Look at the content of the items and refer to Geoff Masters (1988) "Item discrimination: when more is worse", Journal of Educational Measurement, 25:1, 15-29, and www.rasch.org/rmt/rmt72f.htm - RMT 7:2, 289.

2. Don't be intimidated by the statistics. What is your sample size? Is it making the hypothesis test too sensitive? See www.rasch.org/rmt/rmt171n.htm - RMT 17:1, p. 918. Are the mean-squares (chi-squares divided by their degrees of freedom) so close to their expectations that the differences have no substantive implications, despite being significantly unexpected?

3. Are the three items contributing to accurate measurement, or are they distorting measurement? The usual way to check this is to measure the persons with and without these 3 suspect items and cross-plot the person measures. Who is off the diagonal? Which set of measures better represent the abilities of your sample?

4. If these 3 items really are substantively "bad", changing the analytical model will not make them "good". A different model will merely hide the symptoms. So omitting the items is preferable to changing the analytical model.

My best items don't fit!, … Rasch Measurement Transactions, 2004, 18:3 p. 992

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
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
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