Behavior Genetics

, Volume 45, Issue 5, pp 581–596 | Cite as

Nonparametric Estimates of Gene × Environment Interaction Using Local Structural Equation Modeling

  • Daniel A. Briley
  • K. Paige Harden
  • Timothy C. Bates
  • Elliot M. Tucker-Drob
Original Research


Gene × environment (G × E) interaction studies test the hypothesis that the strength of genetic influence varies across environmental contexts. Existing latent variable methods for estimating G × E interactions in twin and family data specify parametric (typically linear) functions for the interaction effect. An improper functional form may obscure the underlying shape of the interaction effect and may lead to failures to detect a significant interaction. In this article, we introduce a novel approach to the behavior genetic toolkit, local structural equation modeling (LOSEM). LOSEM is a highly flexible nonparametric approach for estimating latent interaction effects across the range of a measured moderator. This approach opens up the ability to detect and visualize new forms of G × E interaction. We illustrate the approach by using LOSEM to estimate gene × socioeconomic status interactions for six cognitive phenotypes. Rather than continuously and monotonically varying effects as has been assumed in conventional parametric approaches, LOSEM indicated substantial nonlinear shifts in genetic variance for several phenotypes. The operating characteristics of LOSEM were interrogated through simulation studies where the functional form of the interaction effect was known. LOSEM provides a conservative estimate of G × E interaction with sufficient power to detect statistically significant G × E signal with moderate sample size. We offer recommendations for the application of LOSEM and provide scripts for implementing these biometric models in Mplus and in OpenMx under R.


LOSEM LOESS Kernel regression Gene × environment interaction Cognitive ability 



This research was supported by National Institutes of Health (NIH) research Grant R21-HD069772 to Dr. Tucker-Drob and R21-AA020588 to Dr. Harden. Daniel A. Briley was supported by NIH training Grant T32HD007081. The Population Research Center at the University of Texas at Austin is supported by NIH Center Grant R24HD042849.

Compliance with Ethical Standards

Conflict of interest

Daniel A. Briley, K. Paige Harden, Timothy C. Bates, and Elliot M. Tucker-Drob have declared that they have no conflict of interest.

Human and Animal Rights and Informed Consent

The ECLS-B was approved by state institutional review boards where testing was conducted. All participants provided informed consent before taking part in the study.

Supplementary material

10519_2015_9732_MOESM1_ESM.doc (68 kb)
Supplementary material 1 (DOC 67 kb)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Daniel A. Briley
    • 1
  • K. Paige Harden
    • 1
  • Timothy C. Bates
    • 2
  • Elliot M. Tucker-Drob
    • 1
  1. 1.Department of Psychology and Population Research CenterUniversity of Texas at AustinAustinUSA
  2. 2.Department of PsychologyUniversity of EdinburghEdinburghUK

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