Detecting Prior-Data Disagreement in Bayesian Structural Equation Modeling

Abstract

The choice of prior specification plays a vital role in any Bayesian analysis. Prior-data disagreement occurs when the researcher’s prior knowledge is not in agreement with the evidence provided by the data. We examined the ability of the Data Agreement Criterion (DAC) and Bayes Factor (BF) to detect prior-data disagreement in SEM through a simulation study. The design included four sample size levels and 49 prior specifications. Findings suggested that prior-data disagreement still affects posterior estimates when samples are relatively large. Further, comparing multiple prior specifications sheds more light on the presence of prior-data disagreement than assessing a single prior specification. The DAC was easy to implement but cannot assess interactions between priors within one specification. The BF takes these interactions into account, resulting in a global assessment of prior-data disagreement. However, the BF became challenging to compute with larger sample sizes. Implications for applied researchers are discussed.

Publication
Structural Equation Modeling