Simulating Rasch datasets from known item difficulties and person abilities is straightforward www.rasch.org/rmt/rmt213a.htm
More challenging is simulating Rasch datasets with known marginal scores. Verhelst et al. (2007) achieve this for complete rectangular dichotomous datasets using a Markov-Chain Monte-Carlo (MCMC) algorithm. Its operates on dichotomous data by shuffling observations between rows and columns. The program is implemented as an R package, RaschSampler, which can simulate matrices of up to 1024 rows and 64 columns.
Another approach is to simulate the data using Rasch measures. The dataset can be dichotomous or polytomous, complete or incomplete, and of any size.
1. Compute the marginal scores (persons, items) and counts (polytomous categories) in the generating dataset.
2. In the simulated dataset, impute the extreme observations corresponding to all extreme marginal scores in the generating dataset. Flag those observations as missing in the generating dataset. If there were extreme marginal scores, repeat from 1.
3. Estimate the measures (persons, items, polytomies) for the generating dataset. Rough estimates are good enough. Polytomies: allow for intermediate categories with sampling zeroes.
4. Select a non-missing observation at random in the generating dataset. Simulate its value based on the estimated measures and place it in the matching location in the simulated dataset. Flag that data-point as missing in the generating dataset.
5. Repeat the procedure from 1 until there are no active observations in the original dataset. For dichotomous data, only the measures for one person and one item will need to be re-estimated for each simulated observation. For polytomous data all measures may need to be re-estimated.
When this procedure completes, the simulated dataset will have the same marginal scores and category counts as the original generating dataset.
John Michael Linacre
Verhelst N., Hatzinger R., Mair R. (2007) The Rasch Sampler. Journal of Statistical Software, 20:6. www.jstatsoft.org/v20/i04
Simulating Data from Marginal Scores J.M. Linacre, Rasch Measurement Transactions, 2008, 22:2, 1168
Please help with Standard Dataset 4: Andrich Rating Scale Model
|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|
|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|
|April 29, 2017, Sat., 16:35 to 18:05.||NCME Presidents Invitational Symposium: a new book commemorating Ben Wright's life and career, 16:35 to 18:05, San Antonio, TX, www.ncme.org|
|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|
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|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|
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