Abstract
Purcell (Twin Res 5:554–571, 2002) proposed a bivariate biometric model for testing and quantifying the interaction between latent genetic influences and measured environments in the presence of gene–environment correlation. Purcell’s model extends the Cholesky model to include gene–environment interaction. We examine a number of closely related alternative models that do not involve gene–environment interaction but which may fit the data as well as Purcell’s model. Because failure to consider these alternatives could lead to spurious detection of gene–environment interaction, we propose alternative models for testing gene–environment interaction in the presence of gene–environment correlation, including one based on the correlated factors model. In addition, we note mathematical errors in the calculation of effect size via variance components in Purcell’s model. We propose a statistical method for deriving and interpreting variance decompositions that are true to the fitted model.
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Notes
The candidate moderator need not be an “environmental” variable in the narrow sense of the word. It could represent an environmental variable such as parenting practices or neighborhood crime, or it could also represent another phenotype being modeled as a precursor to the phenotype of interest.
Models for the simulated examples were fitted and tested in Mplus v.4.21 (Muthén and Muthén 2006). Scripts and output files are available for download from the first author’s web site at http://www.health.bsd.uchicago.edu/rathouz/GxM.
Currently available structural equations modeling software such as Mplus (Muthén and Muthén 2006) or Mx (Neale et al. 2003) does not permit estimation of models (6) or (9) owing to nonlinearity of the A and E terms and difficulties of high-dimensional numerical integration. Development of specialized software to fit these models is an area for future development.
This formula is not explicitly stated but is unambiguously implied by Purcell’s formula for rGE given below in (13).
Recall that we omit shared environmental effects C only for simplicity of exposition; these models can be expanded to include C.
R (R Development Core Team 2005) scripts and output files for obtaining the results in this section are available for download from the first author’s web site at http://www.health.bsd.uchicago.edu/rathouz/GxM/.
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The authors thank Wendy Johnson and Robert F. Krueger for insightful comments on the first draft of this article, which dramatically improved subsequent drafts.
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Rathouz, P.J., Van Hulle, C.A., Rodgers, J.L. et al. Specification, Testing, and Interpretation of Gene-by-Measured-Environment Interaction Models in the Presence of Gene–Environment Correlation. Behav Genet 38, 301–315 (2008). https://doi.org/10.1007/s10519-008-9193-4
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DOI: https://doi.org/10.1007/s10519-008-9193-4