Some items are more closely related than others. Comprehension items that address the same written text and arithmetic items requiring the same operation are examples. In Rasch analysis, this is no major source for concern provided there is no extreme systematic dependency between two or a few items. When such dependency does exist, combining the separate items into one partial-credit item may be useful. Low values of the Rasch INFIT statistic signal dependency. When a diagnostically specific investigation of inter-item dependency is required, Fisher's Z is useful.
1)Obtain the Rasch-based standardized residuals for each observation of Person n on item i:
zni = (Observedni - Expectedni)/Standard Errorni
2)Correlate the standardized residuals for all pairs of items i, j across all N persons:
rij = (sum(zni znj) - sum(zni)sum(znj)/N) / N SD(zni) SD(znj)
3)Use Fisher's Z to linearize Pearson correlations:
Zij = 1/2 Loge( (1+rij)/(1-rij) )
4)Draw a histogram of the Fisher Z values. Noticeable positive skew (see Figures) indicates the presence of sets of dependent items. A cluster analysis of the Z matrix will identify the sets. Outlying positive Z values flag pairs or sets of highly dependent items for further investigation.
Quantifying item dependency. Shen L. Rasch Measurement Transactions, 1996, 10:1 p.485
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 | |
---|---|
May 17 - June 21, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
June 12 - 14, 2024, Wed.-Fri. | 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024 |
June 21 - July 19, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
Aug. 5 - Aug. 6, 2024, Fri.-Fri. | 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals |
Aug. 9 - Sept. 6, 2024, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
Oct. 4 - Nov. 8, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
Jan. 17 - Feb. 21, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
May 16 - June 20, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
June 20 - July 18, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com |
Oct. 3 - Nov. 7, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
The URL of this page is www.rasch.org/rmt/rmt101p.htm
Website: www.rasch.org/rmt/contents.htm