Latent Variable Models and Networks: Statistical Equivalence and Testability

Networks are gaining popularity as an alternative to latent variable models for representing psychological constructs. Whereas latent variable approaches introduce unobserved common causes to explain the relations among observed variables, network approaches posit direct causal relations between observed variables. While these approaches lead to radically different understandings of the psychological constructs of interest, recent articles have established mathematical equivalences that hold between network models and latent variable models. We argue that the fact that for any model from one class there is an equivalent model from the other class does not mean that both models are equally plausible accounts of the data-generating mechanism. In many cases the constraints that are meaningful in one framework translate to constraints in the equivalent model that lack a clear interpretation in the other framework. Finally, we discuss three diverging predictions for the relation between zero-order correlations and partial correlations implied by sparse network models and unidimensional factor models. We propose a test procedure that compares the likelihoods of these models in light of these diverging implications. We use an empirical example to illustrate our argument.