Abstract
In this note, we prove that the 3 parameter logistic model with fixed-effect abilities is identified only up to a linear transformation of the ability scale under mild regularity conditions, contrary to the claims in Theorem 2 of San Martín et al. (Psychometrika, 80(2):450–467, 2015a).
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Notes
A typo in the wording of their Theorem was later corrected in an erratum (San Martín, González, & Tuerlinckx, 2015b).
San Martín et al. (2015a) use \(\alpha _j\) for item discrimination, \(\epsilon _i\) for transformed ability, \(\delta _j\) for the complement of guessing and \(\eta _j\) for what is \(\gamma _i\) in this note. Also note that they use i to index persons and j for items.
References
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Acknowledgments
I am grateful to Wim J. van der Linden from Pacific Metrics for drawing my attention to the identification issue of fixed effect 3PL model at IMPS 2015, which made this paper possible.
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Wu, H. A Note on the Identifiability of Fixed-Effect 3PL Models. Psychometrika 81, 1093–1097 (2016). https://doi.org/10.1007/s11336-016-9519-8
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DOI: https://doi.org/10.1007/s11336-016-9519-8