Sample-size calculation for tests of homogeneity

Mixture models are widely used to explain excessive variation in observations that is not captured by standard parametric models, and they lead to suggestive latent structures. The hypothetical latent structure often needs critical examination based on experimental data. It is therefore important to know the sample size needed to ensure a reasonable chance of success. We investigate this issue for the EM-test and the test. They are shown to be asymptotically equivalent and have simple limiting distributions under two sets of local alternatives for commonly used mixture models. We obtain a simple sample-size formula and an associated simulation-based calibration procedure, and we demonstrate via data examples and simulation studies that they provide useful guidance for several common mixture models.