Title: Applying Vuong tests to structural equation models

Authors: Ed Merkle, Dongjun You

Affiliation: University of Missouri

Abstract: The purpose of the talk is to describe and study the theory of
Vuong (1989) for comparing non-nested structural equation models (SEMs).
Researchers may be familiar with the theory's application to count
regression or to latent class models, but implementation difficulties have
prevented full application of the theory to SEM thus far.  We resolve these
difficulties and illustrate the formal statistical tests that result,
allowing us to (i) identify situations where non-nested candidate models
cannot be distinguished from one another, (ii) identify situations where
non-nested models provide different fits to a population of interest, (iii)
obtain confidence intervals associated with differences in information
criteria, and (iv) obtain robust test statistics for nested model
comparison.  We will also discuss the R package nonnest2 (Merkle & You,
2014) that can be used to apply the tests to many classes of models.