Viewed as a statistical device, the Rasch model is one of thousands in current use. One of those thousands most frequently employed is the Pearson Correlation Model.
The Correlation Model
The size of the Pearson product-moment correlation between two variables is frequently reported, sometimes accompanied by whether it is significantly different from 0.00. But rarely reported are:
1) whether the observed correlation departs insignificantly from 1.00, which is perfect correlation. But high correlations, regardless of their statistical significance, could be indicative of collinearity. Near-perfect correlation should be regarded with suspicion.
2) whether the observations violate the assumptions underlying the Correlation Model. Violations are rarely tested explicitly because the correlation model is too useful not to use. Pearson correlations are often reported for data which are known not to meet its assumptions.
The Rasch Model
The Rasch model is similarly too useful not to use. Further, near perfect fit to the Rasch Model should be regarded with suspicion. Empirical processes are uneven. The validity of scientific work has come into question when statistical findings appear to be too perfect.
Taking the same position with regards to the Rasch Model as we do for the Correlation Model, the crucial question is not "Is the correlation statistically 1.0", expressed as "Do the data fit the Rasch model statistically perfectly?" This question has been the focal point of most global fit analysis with the Rasch model. Instead the crucial question becomes "Is the correlation statistically different from 0.00", expressed as "Is there a Rasch dimension which is significantly larger than a point?"
The Rasch dimension reduces to the size of a point when the data are perfectly random. Jacob Cohen (1992) suggests that, for the ratio of explained variance to unexplained variance, 2% is a small effect size, 15% is a medium effect size, and 35% is a large effect size. Recast this as the percentage of total variance explained and 2% is a small effect size, 13% is a medium effect size, and 26% is a large effect size. For comparison, the variance explained by the Rasch measures for the Liking for Science data is 51% [revised, 2008] and for the Knox Cube Test data is 71% [revised, 2008]. Even the variance explained for a relatively central, poorly fitting, NSF survey data set is 30% [revised, 2008]. Rasch papers can routinely report effect statistics, which, if they were the findings of correlation studies, would produce great joy among social scientists.
John M. Linacre
Cohen J. (1992) A Power Primer, Psychological Bulletin, 112, 155-159.
Fit to Models: Rasch Model vs. Correlation Model. Linacre J.M. Rasch Measurement Transactions, 2005, 19:3 p. 1029
|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|
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|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|
|May 24 - June 21, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - 30, 2019, Wed.-Thu.||Measuring and scale construction (with the Rasch Model), University of Manchester, England, https://www.cmist.manchester.ac.uk/study/short/intermediate/measurement-with-the-rasch-model/|
|June 17-19, 2019, Mon.-Wed.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Introduction to Rasch measurement (Trevor Bond, Winsteps), Announcement|
|June 20-21, 2019, Thurs.-Fri.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Advanced Rasch measurement with Facets (Trevor Bond, Facets), Announcement|
|June 28 - July 26, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|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|
|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|
|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|
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