多层贝叶斯结构方程模型的确定性留一聚类交叉验证
Deterministic Leave-One-Cluster-Out Cross-Validation for Multilevel Bayesian Structural Equation Models
- King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
- Universiti Brunei Darussalam（文莱达鲁萨兰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出多层贝叶斯SEM的确定性LOCO交叉验证方法，无需重拟合或蒙特卡洛采样，计算成本低，经模拟及PISA、MIDUS数据验证有效。
AI中文摘要：
我们针对多层高斯贝叶斯结构方程模型（SEM）引入了一种闭式、无需重拟合的留一聚类（LOCO）交叉验证方法，同时对每个嵌套子模型进行预测评分。给定参数时，聚类的条件独立性将删除聚类后的后验分布表示为全后验分布的函数。LOCO预测密度随后为聚类似然的调和均值，可通过INLAvaan计算，INLAvaan是用于贝叶斯SEM的集成嵌套拉普拉斯近似包。我们通过高斯后验下聚类似然倒数的完全指数拉普拉斯近似，闭式计算调和均值期望；候选结构限制通过同一拉普拉斯摘要的高斯条件得出。所得泰勒elpd（预期对数预测密度）评分完全确定，既无需重拟合也无需蒙特卡洛采样，因此不会出现朴素调和均值估计量的方差病态问题。复合对称聚类协方差的直和分解使计算成本与聚类规模无关，远低于暴力重拟合的量级。我们在模拟中通过与暴力重拟合及马尔可夫链蒙特卡洛对比验证了该方法，并在PISA 2022的校园安全氛围数据和MIDUS同胞样本中关联人格与幸福感的16种候选结构上说明了该方法的应用。
英文摘要：
We introduce a closed-form, refit-free procedure for leave-one-cluster-out (LOCO) cross-validation in multilevel Gaussian Bayesian structural equation models (SEMs), together with predictive scoring of every nested submodel. Conditional independence of clusters given the parameters expresses the cluster-deleted posterior as a functional of the full posterior. The LOCO predictive density is then a harmonic mean of the cluster likelihood, computable from a single fit in INLAvaan, the integrated nested Laplace approximation package for Bayesian SEM. We evaluate the harmonic-mean expectation in closed form through a fully exponential Laplace approximation of the reciprocal cluster likelihood under a Gaussian posterior; candidate structural restrictions follow by Gaussian conditioning of the same Laplace summary. The resulting Taylor elpd (expected log predictive density) scores are fully deterministic, requiring neither refitting nor Monte Carlo sampling, so the variance pathology of the naive harmonic-mean estimator does not arise. A direct-sum decomposition of the compound-symmetric cluster covariance makes the cost independent of cluster size, orders of magnitude below brute-force refitting. We validate against brute-force refits and Markov chain Monte Carlo in simulation, and illustrate the procedure on school-safety climate in PISA 2022 and on 16 candidate structures linking personality and well-being in the MIDUS sibling sample.
