ABSTRACT

Posterior Predictive Model Checking (PPMC) is frequently used for model fit evaluation in Bayesian Confirmatory Factor Analysis (BCFA). In standard PPMC procedures, model misfit is quantified by comparing the location of an ML-based point estimate to the predictive distribution of a statistic. When the point estimate is far from the center posterior predictive distribution, model fit is poor. Not included in this approach, however, is the variability of the Maximum Likelihood (ML)-based point estimates. We propose a new method of PPMC based on comparing posterior predictive distributions of a hypothesized and saturated BCFA model. The method uses the predictive distribution of the saturated model as a reference and the Kolmogorov-Smirnov (KS) statistic to quantify the local misfit of hypothesized models. The results of the simulation study suggest that the saturated model PPMC approach was an accurate method of determining local model misfit and could be used for model comparison. A real data example is also provided in this study.

摘要

后验预测模型检查 (PPMC) 经常用于贝叶斯验证因子分析 (BCFA) 中的模型拟合评估。在标准的 PPMC 程序中，模型失配通过将基于 ML 的点估计的位置与统计量的预测分布进行比较来量化。当点估计远离中心后验预测分布时，模型拟合很差。然而，这种方法不包括基于最大似然 (ML) 的点估计的可变性。我们提出了一种基于比较假设和饱和 BCFA 模型的后验预测分布的 PPMC 新方法。该方法使用饱和模型的预测分布作为参考，使用 Kolmogorov-Smirnov (KS) 统计量来量化假设模型的局部失配。仿真研究结果表明，饱和模型PPMC方法是确定局部模型失配的准确方法，可用于模型比较。本研究还提供了一个真实的数据示例。