Abstract

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any combination of discrete and/or continuous responses and their association with a set of predictors. We use the parameter expansion for data augmentation strategy to construct a Markov chain Monte Carlo algorithm for the estimation of the parameters and the latent variables of the model. Based on a centered parameterization of the Gaussian latent variables, we design a fixed-dimensional proposal distribution to update jointly the latent binary vectors of important predictors and the corresponding nonzero regression coefficients. For Gaussian responses and for outcomes that can be modeled as a dependent version of a Gaussian response, this proposal leads to a Metropolis-Hastings step that allows an efficient exploration of the predictors’ model space. The proposed strategy is tested on simulated data and applied to real datasets in which the responses consist of low-intensity counts, binary, ordinal and continuous variables.

摘要

我们开发了一种新颖的贝叶斯方法来选择具有不同类型的多重响应的回归模型中的重要预测变量。稀疏高斯联结回归模型用于解释离散和/或连续响应的任意组合及其与一组预测变量的关联之间的多变量依赖性。我们使用参数扩展数据增强策略构建马尔可夫链蒙特卡罗算法来估计模型的参数和潜在变量。基于高斯潜在变量的中心参数化，我们设计了一个固定维度的提议分布来联合更新重要预测变量的潜在二元向量和相应的非零回归系数。对于高斯响应和可以建模为高斯响应的依赖版本的结果，该提案导致了 Metropolis-Hastings 步骤，允许有效探索预测变量的模型空间。所提出的策略在模拟数据上进行了测试，并应用于真实数据集，其中响应由低强度计数、二进制、序数和连续变量组成。