Products of Variables in Structural Equation Models

Steven M. Boker, Timo von Oertzen, Joshua N. Pritikin, Michael D. Hunter, Timothy R. Brick, Andreas M. Brandmaier, Michael C. Neale

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A general method is introduced in which variables that are products of other variables in the context of a structural equation model (SEM) can be decomposed into the sources of variance due to the multiplicands. The result is a new category of SEM which we call a Products of Variables Model (PoV). Some useful and practical features of PoV models include the estimation of interactions between latent variables, latent variable moderators, manifest moderators with missing values, and manifest or latent squared terms. Expected means and covariances are analytically derived for a simple product of two variables and it is shown that the method reproduces previously published results for this special case. It is shown algebraically that using centered multiplicands results in an unidentified model, but if the multiplicands have non-zero means, the result is identified. The method has been implemented in OpenMx and Ωnyx and is applied in five extensive simulations.

Original languageEnglish (US)
Pages (from-to)708-718
Number of pages11
JournalStructural Equation Modeling
Issue number5
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Decision Sciences
  • General Economics, Econometrics and Finance
  • Sociology and Political Science
  • Modeling and Simulation

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