Diagnostic Techniques For Regression Models
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Diagnostic Techniques for Regression Models
Diagnostics techniques have been developed for the detection of problems arising in the application of regression models. These problems may be associated with violations of one or more assumptions of the model, with the presence of outliers in the data, with the inappropriate choice of the functional form of the model etc. Most of the proposed diagnostic techniques are suitable for the linear model. However, there are several techniques that may be applied to more complex types of models. Our aim is to present the major developments in the area of diagnostic methods for linear regression models, as well as diagnostic methods which are applicable to some more general types of models. The latter include generalized linear models, nonlinear models and errors in variables models.
Regression Diagnostics
Explaining the techniques needed for exploring problems that comprise a regression analysis, and for determining whether certain assumptions appear reasonable, this book covers such topics as the problem of collinearity in multiple regression, non-normality of errors, and discrete data.
Robust Diagnostic Regression Analysis
Author: Anthony Atkinson
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is about using graphs to understand the relationship between a regression model and the data to which it is fitted. Because of the way in which models are fitted, for example, by least squares, we can lose infor mation about the effect of individual observations on inferences about the form and parameters of the model. The methods developed in this book reveal how the fitted regression model depends on individual observations and on groups of observations. Robust procedures can sometimes reveal this structure, but downweight or discard some observations. The novelty in our book is to combine robustness and a forward" " search through the data with regression diagnostics and computer graphics. We provide easily understood plots that use information from the whole sample to display the effect of each observation on a wide variety of aspects of the fitted model. This bald statement of the contents of our book masks the excitement we feel about the methods we have developed based on the forward search. We are continuously amazed, each time we analyze a new set of data, by the amount of information the plots generate and the insights they provide. We believe our book uses comparatively elementary methods to move regression in a completely new and useful direction. We have written the book to be accessible to students and users of statistical methods, as well as for professional statisticians.