Detecting Model Misspecification in Bayesian Piecewise Growth Models

Bayesian estimation has become increasingly more popular with piecewise growth models because it can aid in accurately modeling nonlinear change over time. Recently, new Bayesian approximate fit indices (BRMSEA, BCFI, and BTLI) have been introduced as tools for detecting model (mis)fit. We compare these indices to the posterior predictive p-value (PPP), and also examine the Bayesian information criterion (BIC) and the deviance information criterion (DIC), to identify optimal methods for detecting model misspecification in piecewise growth models. Findings indicated that the Bayesian approximate fit indices are not as reliable as the PPP for detecting misspecification. However, these indices appear to be viable model selection tools rather than measures of fit. We conclude with recommendations regarding when researchers should be using each of the indices in practice.贝叶斯估计（Bayesian estimation）在分段增长模型（piecewise growth models）中的应用愈发广泛，因其可辅助实现随时间非线性变化的精准建模。近年来，新型贝叶斯近似拟合指数（Bayesian approximate fit indices，包含BRMSEA、BCFI与BTLI）被提出，用于检测模型拟合偏差。本研究将上述指数与后验预测p值（posterior predictive p-value，PPP）进行对比，同时考察贝叶斯信息准则（Bayesian information criterion，BIC）与偏差信息准则（deviance information criterion，DIC），以筛选出分段增长模型中检测模型设定偏误的最优方法。研究结果表明，贝叶斯近似拟合指数在检测模型设定偏误时的可靠性不及PPP。不过，此类指数更适合作为可行的模型选择工具，而非拟合度衡量指标。本研究最终针对研究者在实际应用中各类指数的选用时机给出了相关建议。