Finally, analyzing G×E interactions can be computationally intensive. For dichotomous traits, testing G×E interaction under a logistic regression framework requires maximizing the likelihood function numerically; for quantitative traits, testing the interaction with family-based longitudinal data using a mixed-effects model also relies on numerical optimization, both of which are computationally much more extensive than contingency table or regular regression approaches. Bayesian methods are, inherently, computationally demanding as well, but may allow consideration of more complex models. When scaling up to genome-wide data with hundreds of thousands of SNPs, care should be taken to choose an appropriate statistical model, analysis software, and necessary computing hardware. As demonstrated by Shi et al. [2009], mixed-effects models with Kronecker and hierarchical structures yielded comparable model fitness. However, the Kronecker analysis required about 5 minutes for a single model fitting, while the hierarchical model required only 3 seconds, both using SAS PROC MIXED. Due to the parallel nature of the genome-wide scan, cluster computing with tens or hundreds of computing units working simultaneously can significantly reduce the overall computation time. SAS Grid computing enables SAS applications
