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Chunk #6 — Methods and results — Delineation of 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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We determine δij coefficients using the additive genetic G × E regression model for all individuals from Eq. (1). When the β coefficients of Eq. (1) are available, for the subset of individuals with G = 0, plugging the value 0 for the G variable into Eq. (1) eliminates the G and G × E terms and we have: P∣(G=0)=β0+β2E=δ00+δ01E.