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Title: Bivariate copula additive models for location, scale and shape Authors:  Rosalba Radice - Cass Business School (United Kingdom)
Giampiero Marra - University College London (United Kingdom) [presenting]
Abstract: A unified framework is discussed for fitting flexible bivariate copula-based regression models for continuous margins, binary margins and a mixture of the two. The proposed approach allows for the simultaneous estimation of the copula coefficient and marginal distribution parameters (typically location, scale and shape), and for each parameter to be modelled in a regression setting using an additive predictor that comprises different types of covariate effects (e.g. non-linear, random and spatial effects). Parameter estimation is achieved within a penalized likelihood framework using a computationally stable and efficient trust region algorithm with integrated automatic multiple smoothing parameter selection. The proposed approach allows for straightforward inclusion of potentially any parametric marginal distribution and copula function. The models can be easily used via the R package SemiParBIVProbit. The usefulness of the proposal will be illustrated on several case studies drawn from the fields of epidemiology, biostatistics and econometrics.