Improved estimation of the goodness-of-fit measure "pi-star" proposed by Rudas, Clogg, and Lindsay

What is it about?

Several authors pointed out that for large samples the usual measure of goodness-of-fit based on the chi-squared statistic tends to reject fit of models. To overcome this, Rudas, Clogg, and Lindsay (1994) proposed a new goodness-of-fit measure "pi-star" or "mixture index of fit" instead of the conventional chi-squared statistic. However, its sample estimate turned to have an upwards bias (that is, tends to overestimate the population pi-star). Now we worked out a bias-corrected estimate and a new confidence interval for pi-star.

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Why is it important?

In log-linear modelling of contingency tables it is important to see how well a certain model fits to data. Pi-star, among others, can be used to quantify the goodness-of-fit of a model. Biased estimation of pi-star may invalidate the results, therefore reduction of bias is important to increase reliability of statistical analysis.