The problem of model selection uncertainty in structural equation modeling

Model selection in structural equation modeling (SEM) involves using selection criteria to declare one model superior and treating it as a best working hypothesis until a better model is proposed. A limitation of this approach is that sampling variability in selection criteria usually is not considered, leading to assertions of model superiority that may not withstand replication. We illustrate that selection decisions using information criteria can be highly unstable over repeated sampling and that this uncertainty does not necessarily decrease with increases in sample size. Methods for addressing model selection uncertainty in SEM are evaluated, and implications for practice are discussed.