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On the Unidentifiability of the Fixed-Effects 3PL Model

Published online by Cambridge University Press:  01 January 2025

Ernesto San Martín ,
Jorge González  and
Francis Tuerlinckx
Ernesto San Martín*
Affiliation:
Pontificia Universidad Católica de Chile, Measurement Center Mide UC, Ceppe-UC and Université Catholique de Louvain
Jorge González
Affiliation:
Pontificia Universidad Católica de Chile and Measurement Center Mide UC
Francis Tuerlinckx
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Ernesto San Martín, Faculty of Mathematics, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile. E-mail: esanmart@mat.puc.cl
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Abstract

The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL, and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them.

Keywords

consistent estimatoridentified parametersparameters of intereststatistical modelunbiased estimator
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 2 , June 2015 , pp. 450 - 467
Copyright
Copyright © 2014 The Psychometric Society

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