Preface to First Edition - lib

ANALYSIS USING R 129R> myplot(role.fitted1)Probability of agreeing0.0 0.2 0.4 0.6 0.8 1.0Fitted (Males)Fitted (Females)0 5 10 15 20EducationFigure 7.6Fitted (from womensrole_glm_1) and observed probabilities of agreeingfor the womensrole data.are adequate. A comprehensive account of these is given in Collett (2003); herewe shall demonstrate only the use of what is known as the deviance residual.This is the signed square root of the contribution of the ith observation to theoverall deviance. Explicitly it is given by( ( )( )) 1/2 yini − y id i = sign(y i − ŷ i ) 2y i log + 2(n i − y i ) log(7.3)ŷ i n i − ŷ iwhere sign is the function that makes d i positive when y i ≥ ŷ i and negativeelse. In (7.3) y i is the observed number of ones for the ith observation(the number of people who agree for each combination of covariates in ourexample), and ŷ i is its fitted value from the model. The residual providesinformation about how well the model fits each particular observation.© 2010 by Taylor and Francis Group, LLC