Hierarchical Archimedean copula models for the analysis of binary familial data

Archimedean copulas are commonly used in a wide range of statistical models due to their simplicity, manageable analytical expressions, rich choices of generator functions, and other workable properties. However, the exchangeable dependence structure inherent to Archimedean copulas limits its application to familial data, where the dependence among family members is often different. When response variables are binary, modeling the familial associations becomes more challenging due to the stringent constraints imposed on the dependence parameters. This paper proposes hierarchical Archimedean copulas to account for the natural hierarchical dependence structure in familial data and addresses the details in the modeling of binary familial data and the inference based on maximum likelihood estimate. An example showing the flexibility of this powerful tool is also presented with possible extension to other similar studies.