Specification, Testing, and Interpretation of Gene-by-Measured-Environment Interaction Models in the Presence of Gene–Environment Correlation

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.