### 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 (2003, 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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Journal | British Journal of Mathematical and Statistical Psychology |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

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### ASJC Scopus subject areas

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

### Cite this

*British Journal of Mathematical and Statistical Psychology*. https://doi.org/10.1111/bmsp.12118

**Bias-corrected estimation of the Rudas-Clogg-Lindsay mixture index of fit.** / Reiczigel, J.; Ispány, Márton; Tusnády, Gábor; Michaletzky, György; Marozzi, Marco.

Research output: Contribution to journal › Article

*British Journal of Mathematical and Statistical Psychology*. https://doi.org/10.1111/bmsp.12118

}

TY - JOUR

T1 - Bias-corrected estimation of the Rudas-Clogg-Lindsay mixture index of fit

AU - Reiczigel, J.

AU - Ispány, Márton

AU - Tusnády, Gábor

AU - Michaletzky, György

AU - Marozzi, Marco

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 (2003, 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.

AB - 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 (2003, 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.

UR - http://www.scopus.com/inward/record.url?scp=85042531532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042531532&partnerID=8YFLogxK

U2 - 10.1111/bmsp.12118

DO - 10.1111/bmsp.12118

M3 - Article

C2 - 28898399

AN - SCOPUS:85042531532

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

ER -