Equation (2) extends Eq. (1) to the GxE approach by including the b2m and b3 estimates. The b3 estimate is the GWGEI estimate, and it describes the extent to which the effect of a SNP is moderated by the environment (Z). The effect of Z is conditioned on parental mating type (as described by b2mZi), which reduces potential confounding due to gene-environment correlation. That is, if the likelihood of college graduation (E) is higher for those whose parents have a particular genetic makeup (G), then G and E are not independent and GxE parameter estimate may be biased (Jaffee and Price 2007). The use of generalized liner modeling strategies, as opposed to specific software packages such as FBAT, is attractive in that it allows for complex sampling designs, sampling weights, multilevel extensions (possibly including longitudinal mixed extensions), and virtually any way of measuring the phenotype (e.g., binary, count, time to onset, multinomial). This modeling flexibility makes genome-wide analyses more approachable for demographic researchers. This flexibility increases computational demands compared with using specialized software, but advances in the speed of modern computing technology makes this type of work a more viable option for many researchers.
