A mixture of mixture models to detect unity measure errors

The unity measure error is one of the most frequent systematic errors in surveys measuring quantitative variables. In this paper we reinterpret the identification of items in error as a clustering problem where each class is associated with a specific error pattern. In particular we use a two-level mixture approach where each class is modelled as a multivariate Gaussian mixture to allow effective classification in non-normal settings. Finally, an application of the method to the 1997 Italian Labour Cost Survey is reported.