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On the Existence and Uniqueness of JML Estimates for the Partial Credit Model

Published online by Cambridge University Press:  01 January 2025

Lucio Bertoli-Barsotti
Lucio Bertoli-Barsotti*
Affiliation:
University di Bergamo, Italy
*
Requests for reprints should be sent to Prof. Lucio Bertoli-Barsotti, Dipartimento di Matematica, Statistica, Informatica e Applicazioni, Università di Bergamo, Via Dei Caniana, 2, I-24127 Bergamo, Italy. E-mail: lucio.bertoli-barsotti@unibg.it
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Abstract

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis of a simple iterative procedure. The result is proved by using an argument of Haberman (1977).

Keywords

rasch modelpartial credit modelmaximum likelihood estimateexponential familyconvexity.
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 3 , September 2005 , pp. 517 - 531
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

The author wishes to thank the Editor and the anonymous reviewers for their comments that helped to substantially improve the final version of this paper.

This research was supported in part by a MURST grant (ex 60%).

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