Deterministic Leave-One-Cluster-Out Cross-Validation for Multilevel Bayesian Structural Equation Models

2026-08-31

AI Summary

本文提出了一种无需重拟合的确定性留一簇交叉验证方法，用于多层高斯贝叶斯结构方程模型，并通过INLAvaan软件包实现。

Abstract

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.

Problem

• Leave-One-Cluster-Out
• Bayesian Structural Equation Models
• Cross-Validation

Innovation

• closed-form
• refit-free
• leave-one-cluster-out
• harmonic mean
• Laplace approximation