On Examining the Underlying Normal Variable Assumption in Latent Variable Models With Categorical Indicators

A multiple testing approach is outlined that can be used to examine the assumption of underlying normal variables in latent variable models with categorical indicators. The method is based on an application of the increasingly popular Benjamini-Hochberg multiple testing procedure, and is readily applicable with widely circulated software. The discussed method is especially useful for ascertaining this assumption that is very often made in research based on structural equation modeling using models containing discrete outcomes. The described approach is illustrated with numerical data.