Multivariate dependence modeling based on comonotonic factors

Comonotonic latent variables are introduced into general factor models, in order to allow non-linear transformations of latent factors, so that various multivariate dependence structures can be captured. Through decomposing each univariate marginal into several components, and letting some components belong to different sets of comonotonic latent variables, a great variety of multivariate models can be constructed, and their induced copulas can be used to model various multivariate dependence structures. The paper focuses on an extension of Archimedean copulas constructed by Laplace Transforms of positive random variables. The corresponding comonotonic factor models with one set of comonotonic latent variables and multiple sets of comonotonic latent variables are studied. In particular, we propose several parametric comonotonic factor models that are useful in accommodating both within-group and between-group dependence with possible asymmetric tail dependence. Numerical methods for estimation with the resulting copula models are discussed. There is an application using a dataset of body composition measurements to demonstrate the usefulness of the proposed parsimonious dependence models.