Simulating Data from Marginal Scores

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



Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
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Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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