Specification, testing, and interpretation of gene-by-measured-environment interaction models in the presence of gene-environment correlation.

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.