Nonrobustness of the information test in detecting heterogeneity

In data sets that consist of a large number of clusters, a frequent goal of the analysis is to detect whether heterogeneity exists between clusters. A standard approach is to model the heterogeneity in the framework of a mixture model and to derive a score test to detect heterogeneity. The likelihood function, from which the score test derives, depends heavily on the assumed density of the response variable. This paper examines the robustness of the heterogeneity test to misspecification of this density function when there is homogeneity and shows that the test size can be far different from the nominal level.