A tutorial for comparing nonnested latent variables models

Latent variable modeling is a core aspect of research in the social sciences. Frequently, researchers are interested in comparing the fit of multiple models to a set of data in an effort to select the one that seems most plausible statistically. Together with theory, such statistical investigations can help researchers to gain insights into phenomena in a variety of areas such as psychology, education, sociology, and the health sciences. Latent variable model comparisons have traditionally been made using the likelihood ratio test for nested models and information indices for nonnested models. While effective in some circumstances, these techniques each have weaknesses that can limit their utility in practice. Recent work has been done in developing various approaches for comparing nested and nonnested models in a more effective and accurate manner. The purpose of this paper is to describe these methods and to present their use in a tutorial designed for researchers from a wide array of disciplines and experience. The R script used to conduct the analyses is also available in the appendix.