© 1990 by Biometrika Trust
On continuity-corrected residuals in logistic regression
Bellcore, Morristown, New Jersey 07960, U.S.A.
In choosing residuals for logistic regression the two primary candidates are Pearson or linear residuals and deviance residuals; an asymptotic bias correction can be used with the latter. Residuals can also be computed after the arc sine or the Anscombe transformation, and there are residuals which approximate an outlier score statistic (Williams, 1984). Recently Pierce & Schafer (1986) proposed correcting for continuity before computing residuals. They first studied the behaviour of residuals when calculated at the true parameter, unknown in practice, and then argued that when parameter estimates are close to the true values, this same behaviour will be exhibited by residuals calculated at estimates. Our work shows that this two-step approach can be quite misleading. Continuity corrections are detrimental to the approximate normality of residuals, even in the simplest case. Study of graphical displays based on residuals in realistic problems indicates that the bias correction to the deviance is problematic for extreme probabilities. The linear residuals, as well as the unadjusted deviance residuals and the outlier-test residuals, perform well in moderate-sized problems and in both null and contaminated situations.
Key Words: Binomial regression • Deviance component • Generalized linear model • Pearson statistic