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Chunk #17 — Methods — Illustrative example

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Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression.
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We consider regression of the Γ^j coefficients on the γ^j coefficients where the intercept is not constrained to be zero. We fit the linear model: (4)Γ^j=β0E+βEγ^j. (We draw attention to the slight oddity in notation: the Γ^jand γ^j association estimates are the data in this model, and β0E and βE are the coefficients in the regression model; estimates of these coefficients are also denoted by hats –β^0E and β^E.)