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A Note on the Asymptotic Variance-Covariance Matrix of Item Parameter Estimates in the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Dato N. M. de Gruijter
Dato N. M. de Gruijter*
Affiliation:
University of Leyden
*
Requests for reprints should be sent to Dato N. M. de Gruijter, Educational Research Center, Boerhaavelaan 2, 2334 EN Leyden, THE NETHERLANDS.
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Abstract

Lord and Wingersky have developed a method for computing the asymptotic variance-covariance matrix of maximum likelihood estimates for item and person parameters under some restrictions on the estimates which are needed in order to fix the latent scale. The method is tedious, but can be simplified for the Rasch model when one is only interested in the item parameters. This is demonstrated here under a suitable restriction on the item parameter estimates.

Keywords

asymptotic standard errorsinformation matrixmaximum likelihoodRasch model
Type
Notes And Comments
Information
Psychometrika , Volume 50 , Issue 2 , June 1985 , pp. 247 - 249
Copyright
Copyright © 1985 The Psychometric Society

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References

Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Lord, F. M., & Wingersky, M. S. (in press). Sampling variances and covariances of parameter estimates in item response theory. In Weiss, D. J. (Ed.), Proceedings of the Item Response Theory and Computerized Adaptive Testing Conference. Minneapolis, MN: University of Minnesota, Department of Psychology, Computerized Adaptive Testing Laboratory.Google Scholar
Wingersky, M. S., Lord, F. M. (1984). An investigation of methods for reducing sampling error in certain IRT procedures. Applied Psychological Measurement, 8, 347–364.CrossRefGoogle Scholar
Wright, B. D., Douglas, G. A. (1977). Conditional versus unconditional procedures for sample-free item analysis. Educational and Psychological Measurement, 37, 47–60.CrossRefGoogle Scholar