A Mixture Model for Rare and Clustered Populations Under Adaptive Cluster Sampling

Abstract

Rare populations, such as endangered species, drug users and individuals infected by rare diseases, tend to cluster in regions. Adaptive cluster designs are generally applied to obtain information from clustered and sparse populations. The aim of this work is to propose a unit-level mixture model for clustered and sparse populations when the data are obtained from an adaptive cluster sample. Our approach considers heterogeneity among units belonging to different clusters. The proposed model is evaluated using simulated data and a real experiment in which adaptive samples were drawn from an enumeration of a waterfowl species in a 5,000 km2 area of central Florida. The results show that the model is efficient under many settings, even when the level of heterogeneity is low.