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