Cito Research Reports, N Verhelst, et al.

In Cito Report 92-1, N. Verhelst, H. Verstralen and M. Jansen model the problem of correct responses on a timed test:

log_e (Pni1/Pni0) = (Bn + Sn) - Di

where, for all Nn items completed by person n,
Bn is the ability of person n
Sn is the speed of person n
Di is the difficulty of item i

This can be addressed with standard Rasch software by estimating Bn+Sn and Di from the matrix of responses in which unreached items are missing data, and then decomposing Bn+Sn. Following Rasch's 1953 work, Sn can be modelled as a Poisson process, in which
Sn = c + k * log_e (Nn / duration of test)

The scaling factors, c and k, for Sn are obtained by administering both untimed (plenty of time, Sn = 0) and timed tests to some examinees, and finding values for c and k that produce stable Bn estimates across tests. Rasch Measurement would appreciate a note from any researcher attempting the practical application of this model.

In Cito Report 92-2, F. Kamphuis discusses a hierarchical model for measurement over time. Two levels of sampling are involved: occasions within individuals and individuals within a population. A problem is how to combine all the different performances. Kamphuis discovers that a practical procedure is to estimate a Rasch ability for each individual on each occasion. Then an effect size suitable for hierarchical analysis is obtained by dividing each measure by its standard error. This report provides further impetus for researchers to use Rasch measures as the foundation for further analyses.

In Cito Report 92-3, T. Eggen and N. Verhelst investigate the problem of estimating ability with Conditional Maximum Likelihood (CMLE) and Marginal Maximum Likelihood (MMLE) when there is missing response-level data. When the missing data is due to adaptive testing, CMLE estimation fails. This is because not all data patterns are possible. When items are selected based on some background variable, MMLE estimation is problematic. This is because each item is no longer faced by examinees sampled at random from the one population, usually assumed to be normally distributed. The report concludes that the data collection design be considered in selecting between these two estimation algorithms.

Rasch Measurement hopes these authors will expand their work. The next challenge is estimation for large-scale test-equating and computer-adaptive testing where items are selected by obscure rules from an item bank of conceptually unlimited size and administered to a conceptually unlimited number of students, whose distribution may be multi-modal. A comparative, theoretical and practical examination of all Rasch estimation methods for this scenario would be of great value.

In Cito Report 92-4, T. Theunissen addresses the task of constructing effective indices of test quality. The test publishers' favorite, KR- 20, confuses the characteristics of the test items with those of the test sample. Theunissen observes that the item-dependent, but sample- independent, test information function requires summarizing to be useful. He presents two new indices of test quality based on how well a test would rank a user-defined distribution of examinees. Even if these indices do not gain wide acceptance, they help blaze our trail toward better test-quality indices.

Cito Research Reports, N Verhelst, et al. … Rasch Measurement Transactions, 1992, 6:3 p. 239

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 Rating Scale Analysis - free, Wright & Masters
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
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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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