Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T17:14:52.069Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on the Identifiability of Fixed-Effect 3PL Models

Published online by Cambridge University Press:  01 January 2025

Hao Wu Open the ORCID record for Hao Wu [Opens in a new window]
Hao Wu*
Affiliation:
Boston College
*
Correspondence should be made to Hao Wu, Department of Psychology, Boston College, 140 Commonwealth Ave, Chestnut Hill, MA 02467, USA. Email: hao.wu.5@bc.edu
Get access Rights & Permissions [Opens in a new window]

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).

Keywords

item response theory3PL modelidentification

Information

Type
Article
Information
Psychometrika , Volume 81 , Issue 4 , December 2016 , pp. 1093 - 1097
Copyright
Copyright © 2016 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Drton, M. (2009). Likelihood ratio tests and singularities. Annals of Statistics, 37 (2), 979–1012.CrossRefGoogle Scholar
Qin, J., Liang, K.- Y. (2011). Hypothesis testing in a mixture case-control model. Biometrics, 67, 182–193.CrossRefGoogle Scholar
San Martín, E., González, J., Tuerlinckx, F. (2015). On the unidentifiability of the fixed effect 3PL model. Psychometrika, 80 (2), 450–467.CrossRefGoogle ScholarPubMed
San Martín, E., González, J., Tuerlinckx, F. (2015). Erratum to: On the unidentifiability of the fixed effect 3PL model. Psychometrika, 80 (4), 1146CrossRefGoogle Scholar
van der Linden, W. J., Barrett, M. D. (2016). Linking item response model parameters. Psychometrika, 81, 650CrossRefGoogle ScholarPubMed
Wu, H., & Estabrook, C. R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika. doi:10.1007/s11336-016-9506-0.CrossRefGoogle Scholar
Wu, H., Neale, M. C. (2013). On the likelihood ratio tests in bivariate ACDE models. Psychometrika, 78 (3), 441–463.CrossRefGoogle ScholarPubMed