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Bias-corrected estimation of the Rudas-Clogg-Lindsay mixture index of fit.

Authors
  • Reiczigel, Jenő1
  • Ispány, Márton2, 3
  • Tusnády, Gábor3
  • Michaletzky, György4
  • Marozzi, Marco5
  • 1 University of Veterinary Medicine Budapest, Hungary. , (Hungary)
  • 2 University of Debrecen, Hungary. , (Hungary)
  • 3 Alfréd Rényi Institute of Mathematics, Budapest, Hungary. , (Hungary)
  • 4 Eötvös Loránd University, Budapest, Hungary. , (Hungary)
  • 5 University of Venice, Italy. , (Italy)
Type
Published Article
Journal
The British journal of mathematical and statistical psychology
Publication Date
Nov 01, 2018
Volume
71
Issue
3
Pages
459–471
Identifiers
DOI: 10.1111/bmsp.12118
PMID: 28898399
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the lowest proportion of 'contamination' which, if removed from the population or from the sample, makes the fit of the model perfect. The mixture index of fit has been widely used in psychometric studies. We show that the asymptotic confidence limits proposed by Rudas et al. (1994, J. R Stat Soc. Ser. B, 56, 623) as well as the jackknife confidence interval by Dayton (, Br. J. Math. Stat. Psychol., 56, 1) perform poorly, and propose a new bias-corrected point estimate, a bootstrap test and confidence limits for pi-star. The proposed confidence limits have coverage probability much closer to the nominal level than the other methods do. We illustrate the usefulness of the proposed method in practice by presenting some practical applications to log-linear models for contingency tables. © 2017 The British Psychological Society.

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