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 2nd. 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 |
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| Forum | Rasch Measurement Forum to discuss any Rasch-related topic |
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| Coming Rasch-related Events | |
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| June 19-21, 2013, Wed.-Fri. | SIS 2013 Conference on Advances in Latent Variables: Methods, Models and Applications, Brescia, Italy, meetings.sis-statistica.org/index.php/sis2013/ALV |
| July 1 - Nov. 30, 2013, Mon.-Sun. | Online Course: Introduction to Rasch Measurement Theory (D. Andrich, RUMM), www.education.uwa.edu.au/ppl/courses |
| July 5 - Aug. 2, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| July 15, 2013, Monday | Application deadline: UIC Educational Research Methodology online graduate certificate program, www.go.uic.edu/OnlineMESA |
| July 22, 2013, Monday | Submission deadline: 2014 AERA Annual Meeting, Philadelphia PA, www.aera.net |
| Aug.1-5, 2013, Thur.-Mon. | TERA-PROMS Annual Meeting, Kaohsiung, Taiwan, tera.education.nsysu.edu.tw |
| Aug. 9 - Sept. 6, 2013, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Aug. 22, 2013, Thursday. | Symposium in honor of Svend Kreiner, Copenhagen, Denmark, biostat.ku.dk/kreinersymposium |
| Sept. 4-6, 2013, Wed.-Fri. | IMEKO TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences, Genoa, Italy, www.imeko-genoa-2013.it |
| Sept. 13 - Oct. 11, 2013, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 18-20, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 23-25, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 26-27, 2013, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Oct. 18 - Nov. 15, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
| Oct. 20 - Oct. 25, 2013, Sun.-Fri. | International Association for Educational Assessment (IAEA) 39th Annual Conference, Tel Aviv, Israel, www.iaea-2013.com |
| Dec. 11-13, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| March 12-14, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| April 3-7, 2014, Thurs.-Mon. | AERA Annual Meeting, Philadelphia PA, www.aera.net |
| May 14-16, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| May 19-21, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| July 4 - Aug. 1, 2014, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| Aug. 8 - Sept. 5, 2014, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Sept. 10-12, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 12 - Oct. 10, 2014, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 15-17, 2014, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 18-19, 2014, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
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