2DkcTXceO

R.D. Cook 101no one sought my acquiescence. In 1982 I coauthored a fairly comprehensiveresearch monograph on the state of diagnostic methods (Cook and Weisberg,1982).Encouraged by the wide acceptance of Cook’s Distance and my other diagnosticcontributions, and aided by a year-long fellowship from the MathematicsResearch Center at the University of Wisconsin, I continued working indiagnostics with the goal of developing local differential geometric measuresthat might detect various influential characteristics of a generic likelihoodbasedanalysis. In 1986 I read before the Royal Statistical Society a paper onalocallikelihood-basedtechniqueforthedevelopmentofdiagnosticstodetectinfluential aspects of an analysis (Cook, 1986).Today models can be and often are much more complicated than thoselikely entertained by Fisher or in common use around the time that I wasearnestly working on influence diagnostics. As a consequence, the methodsdeveloped prior to the 1990s are generally not applicable in more complicatedcontemporary contexts, and yet these contexts are no less affected by influentialobservations. Intricate models are prone to instability and the lack ofproper influence diagnostics can leave a cloud of doubt about the strength ofan analysis. While influence diagnostics have been keeping pace with modeldevelopment largely through a series of important papers by Hongtu Zhu andhis colleagues (Zhu et al., 2007, 2012), methods to address other diagnosticissues, or issues unique to a particular modeling environment, are still laggingfar behind. Personally, I am reluctant to accept findings that are notaccompanied by some understanding of how the data and model interacted toproduce them.9.2.2 Diagnostics more generallyAsubstantialbatteryofdiagnosticmethodsforregressionwasdevelopedduringthe 1970s and 1980s, including transformation diagnostics, various graphicaldiagnostics like residual plots, added variable plots (Cook and Weisberg,1982), partial residual plots and CERES plots for predictor transformations(Cook, 1993), methods for detecting outliers and influential observations, anddiagnostics for heteroscedasticity (Cook and Weisberg, 1983). However, it wasunclear how these methods should be combined in a systematic way to aid ananalysis, particularly since many of them addressed one issue at a time. Forinstance, diagnostics for heteroscedasticity required that the mean functionbe correct, regardless of the fact that an incorrect mean function and homoscedasticerrors can manifest as heteroscedasticity. Box’s paradigm (Box,1980) for model criticism was the most successful of the attempts to bringorder to the application of diagnostic methods and was rapidly adopted bymany in the field. It consists essentially of iteratively improving a model basedon diagnostics: an initial model is posited and fitted to the data, followed byapplications of a battery of diagnostic methods. The model is then modified