Preface to First Edition - lib

132 LOGISTIC REGRESSION AND GENERALISED LINEAR MODELSR> res plot(predict(womensrole_glm_2), res,+ xlab="Fitted values", ylab = "Residuals",+ ylim = max(abs(res)) * c(-1,1))R> abline(h = 0, lty = 2)Residuals−2 −1 0 1 2−3 −2 −1 0 1 2 3Fitted valuesFigure 7.9Plot of deviance residuals from logistic regression model fitted to thewomensrole data.The variance function of a GLM captures how the variance of a responsevariable depends upon its mean. The general form of the relationship isVar(response) = φV (µ)where φ is constant and V (µ) specifies how the variance depends on the mean.For the error distributions considered previously this general form becomes:Normal: V (µ) = 1, φ = σ 2 ; here the variance does not depend on the mean.Binomial: V (µ) = µ(1 − µ), φ = 1.© 2010 by Taylor and Francis Group, LLC