Estimating and interpreting latent variable interactions: A tutorial for applying the latent moderated structural equations method

Julie Maslowsky, Justin Jager, Douglas Hemken

Research output: Contribution to journalArticle

162 Scopus citations

Abstract

Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS) method is one that is built into Mplus software. The potential utility of this method is limited by the fact that the models do not produce traditional model fit indices, standardized coefficients, or effect sizes for the latent interaction, which renders model fitting and interpretation of the latent variable interaction difficult. This article compiles state-of-the-science techniques for assessing LMS model fit, obtaining standardized coefficients, and determining the size of the latent interaction effect in order to create a tutorial for new users of LMS models. The recommended sequence of model estimation and interpretation is demonstrated via a substantive example and a Monte Carlo simulation. Finally, extensions of this method are discussed, such as estimating quadratic effects of latent factors and interactions between latent slope and intercept factors, which hold significant potential for testing and advancing developmental theories.

Original languageEnglish (US)
Pages (from-to)87-96
Number of pages10
JournalInternational Journal of Behavioral Development
Volume39
Issue number1
DOIs
StatePublished - Jan 20 2015

Keywords

  • latent variables
  • methodology
  • structural equation modeling

ASJC Scopus subject areas

  • Social Psychology
  • Education
  • Developmental and Educational Psychology
  • Social Sciences (miscellaneous)
  • Developmental Neuroscience
  • Life-span and Life-course Studies

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