Homogeneous data clusters in interlaboratory studies

There are many interlaboratory studies for which the commonly employed random effects model is not adequate as the heterogeneous discrepant data indicate quite different (larger) variances for some participating laboratories. Motivated by such examples we provide methods to choose a more flexible paradigm with a number of different clusters each consisting of laboratories having the same heterogeneity variance. Then the largest homogeneous (consistent) data subset corresponds to zero heteroscedasticity. The paper is focused on its determination when all heterogeneous observations are put into one class so that there is just one positive heterogeneity variance. The likelihood based procedures which determine the clusters arc obtained in the general case. A Bayes rule against a non-informative prior is suggested for model averaging.