ABSTRACT

The deviance information criterion (DIC) is widely used to select the parsimonious, well-fitting model. We examined how priors impact model complexity (pD) and the DIC for Bayesian CFA. Study 1 compared the empirical distributions of pD and DIC under multivariate (i.e., inverse Wishart) and separation strategy (SS) priors. The former treats the covariance matrix ${\mathbf{\Phi }}_{\xi }$ as “a” parameter, and the latter places marginal priors on factor variances and correlations. Study 1 revealed that SS priors for the factor covariance matrix led to larger pD and smaller DIC as compared to IW priors. Study 2 evaluated the DIC’s ability to properly detect model misspecification under different prior settings. The ability to select the correct model improved when SS priors were implemented as compared to $IW(\mathbf{I},\nu )$ priors. We also uncovered that the DIC can better detect under-fitting as misfit than over-fitting. Practical guidelines for implementation and future research directions are discussed.

摘要

偏差信息准则 (DIC) 被广泛用于选择简约、拟合良好的模型。我们研究了先验如何影响模型复杂性 (pD) 和贝叶斯 CFA 的 DIC。研究 1 比较了 pD 和 DIC 在多元（即逆 Wishart）和分离策略 (SS) 先验条件下的经验分布。前者处理协方差矩阵${\mathbf{\Phi }}_{\xi }$作为“a”参数，后者将边际先验放在因子方差和相关性上。研究 1 表明，与 IW 先验相比，因子协方差矩阵的 SS 先验导致更大的 pD 和更小的 DIC。研究 2 评估了 DIC 在不同先前设置下正确检测模型错误指定的能力。与之前相比，当实施 SS 先验时，选择正确模型的能力得到提高$\mathrm{一世}W(\mathbf{一世},\nu )$先验。我们还发现，与过拟合相比，DIC 可以更好地将欠拟合检测为失配。讨论了实施的实用指南和未来的研究方向。