Comparing Alternative Biometric Models with and without Gene-by-Measured Environment Interaction in Behavior Genetic Designs: Statistical Operating Characteristics.

To extend Purcell's well known ACE model in testing gene by measured environment interactions (GxM) in behavior genetic designs, Rathouz et al. considered a broader class of models for quantifying and testing such interactions. Only a sub-group of these extended models have been investigated for their statistical operating characteristics by Van Hulle et al. due to lack of closed form likelihood. With an estimation procedure developed using numerical techniques in a companion paper, we study statistical operating characteristics of these extended models, especially those with non-linear effects. Type I error analysis shows the likelihood ratio test for GxM to be conservative in testing models extended from the bivariate Cholesky model, and to be liberal for models extended from the bivariate correlated factors model. Parameter estimation for all models is very good, with little bias exhibited for most models and parameters. Comparisons among alternative models under various simulated conditions show that it is relatively more difficult to confirm the existence of gene by environment interactions versus to detect non-linear effects which exclude such interactions.