Pair-copula Models for Analyzing Family Data

Abstract

The construction of multivariate models for analyzing family data can be challenging due to the various dependencies between family members. These models typically have parameters that are subject to intricate and stringent constraints, which make it more difficult to arrive at a proper estimation of these model parameters. Recently, vines and pair-copula constructions have been utilized in order to simplify construction of multivariate models for both continuous and discrete data. The pair-copula models break down the hierarchy of dependence into vines and employ bivariate or pair-copulas as “building bricks” to generate appropriate multivariate distributions. This paper discusses pair-copula methods to model the convoluted dependence structure and proposes using a C-Vine type copula to model the dependence among family members. Analysis of actual, real-world family data is presented to illustrate our models and estimation procedures.