On the Unidentifiability of the Fixed-Effects 3PL Model

San Martin Gutiérrez, Ernesto;Tuerlinckx, Francis;González, Jorge
(2014) Psychometrika — p. 1-18 (2014)

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Authors
  • San Martin Gutiérrez, ErnestoUCLouvain
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  • Tuerlinckx, Francis
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  • González, Jorge
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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. © 2014 The Psychometric Society.
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San Martin Gutiérrez, E., Tuerlinckx, F., & González, J. (2014). On the Unidentifiability of the Fixed-Effects 3PL Model. Psychometrika, 1-18. https://doi.org/10.1007/s11336-014-9404-2 (Original work published 2014)