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A maximum likelihood fit of a logistic regression model (and other similar models) is extremely sensitive to outlying responses and extreme points in the design space. We develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit. The elements of the fitting process which constitute the usual output (parameter estimates, standard errors, residuals, etc.) will be used for this purpose. With a properly designed computing package for fitting the usual maximum-likelihood model, the diagnostics are essentially "free for the asking." In particular, good data analysis for logistic regression models need not be expensive or time-consuming.