The Gaussian chain graph model simultaneously parametrizes (i) the direct effects of $p$ predictors on $q$ outcomes and (ii) the residual partial covariances between pairs of outcomes. We introduce a new method for fitting sparse Gaussian chain graph models with spike-and-slab LASSO (SSL) priors. We develop an Expectation Conditional Maximization algorithm to obtain sparse estimates of the $p \times q$ matrix of direct effects and the $q \times q$ residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes individual model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior contraction rate for our model, buttressing our method's excellent empirical performance with strong theoretical guarantees. Using our method, we estimated the direct effects of diet and residence type on the composition of the gut microbiome of elderly adults.

翻译：高斯链图模型同时参数化了 (i) $p$ 个预测变量对 $q$ 个结果的直接效应，以及 (ii) 结果对之间的残差部分协方差。我们提出了一种新方法，利用spike-and-slab LASSO (SSL) 先验来拟合稀疏高斯链图模型。我们开发了一种期望条件最大化算法，以获得 $p \times q$ 直接效应矩阵和 $q \times q$ 残差精度矩阵的稀疏估计。该算法迭代求解一系列带有自适应惩罚的惩罚最大似然问题，这些惩罚会逐步过滤掉可忽略的回归系数和部分协方差。由于我们的方法对单个模型参数进行自适应惩罚，因此在模拟数据上，该方法优于固定惩罚的竞争方法。我们为模型建立了后验收缩率，为该方法卓越的实证性能提供了强有力的理论保证。利用该方法，我们估计了饮食和居住类型对老年人群肠道微生物组组成的直接效应。