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The Three Basic Types of Residuals for a Linear Model
Author(s) -
Haslett John,
Haslett Stephen J.
Publication year - 2007
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2006.00001.x
Subject(s) - covariance , residual , mathematics , linear model , contrast (vision) , econometrics , multivariate statistics , general linear model , statistics , studentized residual , perspective (graphical) , method of mean weighted residuals , computer science , algorithm , nonlinear system , physics , geometry , quantum mechanics , galerkin method , artificial intelligence
Summary We consider residuals for the linear model with a general covariance structure. In contrast to the situation where observations are independent there are several alternative definitions. We draw attention to three quite distinct types of residuals: the marginal residuals, the model‐specified residuals and the full‐conditional residuals. We adopt a very broad perspective including linear mixed models, time series and smoothers as well as models for spatial and multivariate data. We concentrate on defining these different residual types and discussing their interrelationships. The full‐conditional residuals are seen to play several important roles.