Department of Statistics, London School of Economics, London, UK.
Br J Math Stat Psychol. 2023 Nov;76(3):559-584. doi: 10.1111/bmsp.12314. Epub 2023 Jul 4.
The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive -values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework presented in the paper focuses on the approximate zero approach (Psychological Methods, 17, 2012, 313), which involves formulating certain parameters (such as factor loadings) to be approximately zero through the use of informative priors, instead of explicitly setting them to zero. The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a list of guidelines we provide, one can investigate whether the hypothesised model is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for BSEM. The proposed tools can be applied to models for both continuous and binary data. The modelling of categorical and non-normally distributed continuous data is facilitated with the introduction of an item-individual random effect. We study the performance of the proposed methodology via simulation experiments as well as real data on the 'Big-5' personality scale and the Fagerstrom test for nicotine dependence.
本文提出了一种新的模型评估范式，旨在解决贝叶斯结构方程建模（BSEM）中后验预测值的缺陷，后验预测值是 BSEM 中拟合度的默认度量标准。本文提出的模型框架侧重于近似零方法（Psychological Methods, 17, 2012, 313），该方法通过使用信息先验，将某些参数（如因子载荷）设定为近似为零，而不是将其明确设置为零。所引入的模型评估过程监控拟合模型的样本外预测性能，并且结合我们提供的一系列准则，可以调查假设模型是否得到数据的支持。我们将评分规则和交叉验证纳入 BSEM 的现有模型评估指标中进行补充。所提出的工具可应用于连续数据和二分类数据的模型。通过引入项目个体随机效应，可以方便地对分类数据和非正态分布的连续数据进行建模。我们通过模拟实验以及“大五”人格量表和尼古丁依赖 Fagerstrom 测试的真实数据研究了所提出方法的性能。
