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On the Loss of Information in Conditional Maximum Likelihood Estimation of Item Parameters

Published online by Cambridge University Press:  01 January 2025

Theo J. H. M. Eggen
Theo J. H. M. Eggen*
Affiliation:
Cito, National Institute for Educational Measurement
*
Requests for reprints should be sent to Theo J.H.M. Eggen, Cito, P. O. Box 1034, 6801 MG Arnhem, The Netherlands. E-mail: [email protected]
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Abstract

In item response models of the Rasch type (Fischer & Molenaar, 1995), item parameters are often estimated by the conditional maximum likelihood (CML) method. This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML (joint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency in the use of information of CML to JML and to MML in several comparisons is always larger than 93%, and in tests with a length of 20 items or more, larger than 99%.

Keywords

conditional maximum likelihoodloss of informationF-informationRasch modelsitem parameter estimation
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 337 - 362
Copyright
Copyright © 2000 The Psychometric Society

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