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Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach

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Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach

Content Provider	Springer Nature Link
Author	Klein, Nadja Kneib, Thomas
Copyright Year	2015
Abstract	While most regression models focus on explaining distributional aspects of one single response variable alone, interest in modern statistical applications has recently shifted towards simultaneously studying multiple response variables as well as their dependence structure. A particularly useful tool for pursuing such an analysis are copula-based regression models since they enable the separation of the marginal response distributions and the dependence structure summarised in a specific copula model. However, so far copula-based regression models have mostly been relying on two-step approaches where the marginal distributions are determined first whereas the copula structure is studied in a second step after plugging in the estimated marginal distributions. Moreover, the parameters of the copula are mostly treated as a constant not related to covariates and most regression specifications for the marginals are restricted to purely linear predictors. We therefore propose simultaneous Bayesian inference for both the marginal distributions and the copula using computationally efficient Markov chain Monte Carlo simulation techniques. In addition, we replace the commonly used linear predictor by a generic structured additive predictor comprising for example nonlinear effects of continuous covariates, spatial effects or random effects and furthermore allow to make the copula parameters covariate-dependent. To facilitate Bayesian inference, we construct proposal densities for a Metropolis–Hastings algorithm relying on quadratic approximations to the full conditionals of regression coefficients avoiding manual tuning. The performance of the resulting Bayesian estimates is evaluated in simulations comparing our approach with penalised likelihood inference, studying the choice of a specific copula model based on the deviance information criterion, and comparing a simultaneous approach with a two-step procedure. Furthermore, the flexibility of Bayesian conditional copula regression models is illustrated in two applications on childhood undernutrition and macroecology.
Starting Page	841
Ending Page	860
Page Count	20
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	26
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2015-06-14
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Archimedean copulas Generalised Metropolis–Hastings algorithm Gaussian copula Marginal distribution Penalised splines Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach

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