Dependence of Gene-by-Environment Interactions (GxE) on Scaling: Comparing the Use of Sum Scores, Transformed Sum Scores and IRT Scores for the Phenotype in Tests of GxE.

Estimates of gene-environment interactions (GxE) in behavior genetic models depend on how a phenotype is scaled. Inappropriately scaled phenotypes result in biased estimates of GxE and can sometimes even suggest GxE in the direction opposite to its true direction. Previously proposed solutions are mathematically complex, computationally demanding and may prove impractical for the substantive researcher. We, therefore, evaluated two simple-to-use alternatives: (1) straightforward non-linear transformation of sum scores and (2) factor scores from an appropriate item response theory (IRT) model. Within Purcell's (2002) GxM framework, both alternatives provided less biased parameter estimates, and improved false and true positive rates than using a raw sum score. These approaches are, therefore, recommended over using raw sum scores in tests of GxE. Circumstances under which IRT factor scores versus transformed sum scores should be preferred are discussed.