Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach
Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach
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DOI：
10.1007/s11222-015-9573-6
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发表时间：
2016-07
影响因子：
2.2
通讯作者：
N. Klein;T. Kneib
中科院分区：
文献类型：
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作者：
N. Klein;T. Kneib
虽然大多数回归模型专注于单独解释一个响应变量的分布方面，但现代统计应用的兴趣最近已转向同时研究多个响应变量及其依赖性结构。用于进行此类分析的一个特别有用的工具是基于 copula 的回归模型，因为它们能够分离边际响应分布和特定 copula 模型中总结的依赖结构。然而，到目前为止，基于 copula 的回归模型大多依赖于两步方法，其中首先确定边缘分布，而在插入估计的边缘分布后，第二步研究 copula 结构。此外，连接函数的参数大多被视为与协变量无关的常数，并且大多数边际回归规范仅限于纯线性预测变量。因此，我们提出使用计算高效的马尔可夫链蒙特卡罗模拟技术对边缘分布和联结函数进行同步贝叶斯推理。此外，我们用通用的结构化加性预测器替换常用的线性预测器，该预测器包括例如连续协变量的非线性效应、空间效应或随机效应，并且还允许使 copula 参数依赖于协变量。为了促进贝叶斯推理，我们构建了 Metropolis-Hastings 算法的建议密度，该算法依赖于回归系数完整条件的二次逼近，避免了手动调整。在模拟中评估所得贝叶斯估计的性能，将我们的方法与惩罚似然推理进行比较，研究基于偏差信息标准的特定联结模型的选择，并将同时方法与两步程序进行比较。此外，贝叶斯条件联结回归模型的灵活性在儿童营养不良和宏观生态学的两个应用中得到了说明。
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.