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Consistent Estimation in the Rasch Model based on Nonparametric Margins

Published online by Cambridge University Press:  01 January 2025

Dean Follmann
Dean Follmann*
Affiliation:
National Heart, Lung, and Blood Institute Biostatistics Research Branch
*
Requests for reprints should be sent to Dean Foltmann, NHLBI, Rm 2All, 7550 Wisconsin Avenue, Bethesda MD 20892.
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Abstract

Consider the class of two parameter marginal logistic (Rasch) models, for a test of m True-False items, where the latent ability is assumed to be bounded. Using results of Karlin and Studen, we show that this class of nonparametric marginal logistic (NML) models is equivalent to the class of marginal logistic models where the latent ability assumes at most (m + 2)/2 values. This equivalence has two implications. First, estimation for the NML model is accomplished by estimating the parameters of a discrete marginal logistic model. Second, consistency for the maximum likelihood estimates of the NML model can be shown (when m is odd) using the results of Kiefer and Wolfowitz. An example is presented which demonstrates the estimation strategy and contrasts the NML model with a normal marginal logistic model.

Keywords

nonparametricEM algorithmconsistencyidentifiabilitymarginal logistic modellatent abilityitem analysisRasch model
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 4 , December 1988 , pp. 553 - 562
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

This research was supported by NIMH traning grant, 2 T32 MH 15758-06 and by ONR contract N00014-84-K-0588. The author would like to thank Diane Lambert, John Rolph, and Stephen Fienberg for their assistance. Also, the comments of the referees helped to substantially improve the final version of this paper.

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