Understanding the Deviance Information Criterion for SEM: Cautions in Prior Specification

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 (sic)(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 IWoI;.THORN 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.

Automated summary

The study compared the impact of different priors on model complexity and DIC, revealing that SS priors led to larger pD and smaller DIC compared to IW priors. Additionally, the DIC was found to better detect model misspecification under SS priors compared to IW priors.