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 <i>p</i>-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）与分段增长模型（piecewise growth models）的结合愈发受到青睐，因其能够助力精准刻画随时间推移的非线性变化特征。近期，学界提出了三类新型贝叶斯近似拟合指数（Bayesian approximate fit indices，BRMSEA、BCFI与BTLI），用于检测模型的拟合优劣。本研究将这些指数与后验预测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），以甄别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设定偏误方面的可靠性不及PPP，但这类指数更适合作为模型选择工具而非拟合优劣的衡量标准。最后，本文针对研究者在实践中应如何选用各类指数给出了建议。