Clusters with random size: maximum likelihood versus weighted estimation

Abstract

There are many contemporary designs that do not use a random sample of a fixed, a priori determined size. In case of informative cluster sizes, the cluster size is influenced by the the cluster’s data, but here we cope with some issues that even occur when the cluster size and the data are unrelated. First, fitting models to clusters of varying sizes is often more complicated than when all cluster have the same size. Secondly, in such cases, there usually is no so-called complete sufficient statistic (Molenberghs et al., 2014).