Bias‐corrected estimation of the Rudas–Clogg–Lindsay mixture index of fit

• Published in: British journal of mathematical & statistical psychology Vol. 71; no. 3; pp. 459 - 471
• Main Authors: Reiczigel, Jenő, Ispány, Márton, Tusnády, Gábor, Michaletzky, György, Marozzi, Marco
• Format: Journal Article
• Language: English
• Published: England British Psychological Society 01.11.2018
• Subjects: Bias; bootstrap; Computer Simulation; confidence interval; Confidence intervals; Confidence limits; Contingency; Data Interpretation, Statistical; Goodness of fit; Humans; Models, Statistical; pi‐star; Probability; Psychometrics; RCL mixture index of fit; Regression analysis; Statistical analysis; two‐point mixture model index; pi-star; psychometrics; two-point mixture model index; confidence interval; RCL mixture index of fit; bootstrap
• ISSN: 0007-1102; 2044-8317; 2044-8317
• DOI: 10.1111/bmsp.12118

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.