### 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.

Original language | English |
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Pages (from-to) | 459-471 |

Number of pages | 13 |

Journal | British Journal of Mathematical and Statistical Psychology |

Volume | 71 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 2018 |

### Keywords

- RCL mixture index of fit
- bootstrap
- confidence interval
- pi-star
- psychometrics
- two-point mixture model index

### ASJC Scopus subject areas

- Statistics and Probability
- Arts and Humanities (miscellaneous)
- Psychology(all)

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## Cite this

*British Journal of Mathematical and Statistical Psychology*,

*71*(3), 459-471. https://doi.org/10.1111/bmsp.12118