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

Rudas, Clogg and Lindsay (1994) introduced the so-called mixture index of fit, also known as pi-star (*), for quantifying 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) as well as the jackknife confidence interval by Dayton (2003) perform poorly, and propose a new bias-corrected point estimate, a bootstrap test and confidence limits for the pi-star. The proposed confidence limits have coverage probability much closer to the nominal level than the other methods do. We illustrate that the proposed method is useful in practice by presenting some practical applications to loglinear models for contingency tables.

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 (*), 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 etal. (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.