A SAS Solution to Simulate a Rasch Computerized Adaptive Test

As far as we know, few or any software programs are currently available to simulate adaptive testing. One of them is POSTSIM distributed by Assessment Systems Corporation. This software package is mostly limited by its inability to allow users to modify the program or to add new routines. In fact, scientists exploring the characteristics of adaptive tests usually develop these programs themselves and for themselves. Consequently, the research community's access to them is difficult. Also, when available, they are not versatile, neither is the source code that goes with them in order to favor adaptations.

To palliate this situation and support adaptive testing research, SIMCAT 1.0, a SAS solution, was proposed (Raîche and Blais, 2006c). A preliminary version of this program had been used by Raîche and Blais (2001) to study the sampling distribution of the proficiency level in adaptive testing according to two stopping rules: taking into account the number of administered items and the standard error of the estimated proficiency level. The new version gives access to improvements as regards to the program versatility and to new proficiency level estimation methods. The Rasch dichotomous response model is the one retained.

Expected a posteriori proficiency level estimation method (EAP) is applied to compute estimated provisory and final proficiency level. The new proficiency level estimation methods are all adaptive modifications brought to the EAP method (Raîche and Blais, 2001, 2006b). These methods are all adaptive in the a priori proficiency level estimation, the proficiency level estimation bias correction, the integration interval, or a combination of them. The use of these adaptive EAP estimation methods diminishes considerably the shrinking, and so biasing, effect of the estimated a priori proficiency level encountered when this a priori is fixed at a constant value independently of the previously computed value of the proficiency level.

Another of the program's peculiarity is its feasibility to compare theoretical values of the standard error, skewness, and kurtosis of the estimated proficiency level with the empirical values of these statistics. This according to predetermined sampling distributions of the estimated proficiency level.

The program, a 20 pages manual describing how to use it with a sample of results and the source code are available from by email: raiche.gilles -at- uqam.ca

Gilles Raîche, Université du Québec à Montréal
Jean-Guy Blais, Université de Montréal
Martin Riopel, Université du Québec à Montréal

Blais, J.-G. and Raîche, G. (2006a). Features of the estimated sampling distribution of the ability estimate in computerized adaptive testing according to two stopping rules. In M. Garner, G. Engelhard, M. Wilson and W. Fisher (Eds.): Advances in Rasch Measurement. Volume 1. Maple Grove, MN: JAM Press.
Raîche, G. and Blais, J.-G. (2006b). Considerations about expected a posteriori estimation in adaptive testing : adaptive a priori, adaptive correction for bias, and adaptive integration interval. In M. Garner, G. Engelhard, M. Wilson and W. Fisher (Eds.): Advances in Rasch Measurement. Volume 1. Maple Grove, MN: JAM Press.
Raîche, G. and Blais, J.-G. (2006c). SIMCAT 1.0 - A SAS Computer Program for Simulating Computer Adaptive Testing Applied Psychological Measurement. Applied Psychological Measurement, 30(1), 60-61.
Raîche, G., and Blais, J.-G. (2001). [Study of the sampling distribution of the estimated proficiency level in Rasch-based adaptive testing according to two stopping rules]. Mesure et évaluation en éducation 14(2-3), 23-39.

A SAS Solution to Simulate a Rasch Computerized Adaptive Test, Raîche G., Blais J.-G., Riopel M. … Rasch Measurement Transactions, 2006, 20:2 p. 1061

Rasch Publications
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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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