The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive $p-$values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework of the paper focuses on the approximate zero approach, according to which parameters that would before set to zero (e.g. factor loadings) are now formulated to be approximate zero via informative priors (Muthen and Asparouhov, 2012). 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 Bayesian SEM. The proposed tools can be applied to models for both categorical and continuous data. The modelling of categorical and non-normally distributed continuous data is facilitated with the introduction of an item-individual random effect that can also be used for outlier detection. We study the performance of the proposed methodology via simulations. The factor model for continuous and binary data is fitted to data on the `Big-5' personality scale and the Fagerstrom test for nicotine dependence respectively.
翻译:本文提出了一个新的模型评估模式,旨在解决后后继预测值美元-美元价值的缺陷,为贝叶西亚结构方程模型(BSEM)提供适合巴伊西亚结构方程模型(BSEM)的默认衡量标准。文件的模型框架侧重于近似零方法,根据这一方法,在设定为零之前的参数(例如要素负荷)现在通过信息前先行(Muthen和Asparouhov,2012年)被确定为约为零。引入的模型评估程序将监测装配模型的模外预测性能,并连同我们提供的一系列准则一起,可以调查假设模型是否得到数据的支持。我们采用了评分规则和交叉校验法,以补充巴伊西亚SEM的现有模型评估标准。拟议工具可以适用于绝对数据和连续数据的模型。采用绝对和非正常分布连续数据的建模便利于采用可用于外部检测的物品-个人随机效应。我们通过模拟来研究拟议方法的性能表现。用于连续和双读数据模型的成份数模型,用于`B'的性磁度测试。