Chunk #20 — Methods and results — A reparameterization of the equation to address the problem

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Testing for measured gene-environment interaction: problems with the use of cross-product terms and a regression model reparameterization solution.

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One approach is to recode the genotype data into three orthogonal components, taking the values: H0=(G−1)(G−2)∕2={1,0,0},H1=−G(G−2)∕2={0,1,0},H2=G(G−1)∕2={0,0,1}. (2)P=H0(δ00+δ01E)+H1(δ10+δ11E)+H2(δ20+δ21E).