General Classes of Influence Measures for Multivariate Regression

@article{Barrett1992GeneralCO,
  title={General Classes of Influence Measures for Multivariate Regression},
  author={Bruce E. Barrett and Robert F. Ling},
  journal={Journal of the American Statistical Association},
  year={1992},
  volume={87},
  pages={184-191}
}
Abstract Many of the existing measures for influential subsets in univariate ordinary least squares (OLS) regression analysis have natural extensions to the multivariate regression setting. Such measures may be characterized by functions of the submatrices H I of the hat matrix H, where I is an index set of deleted cases, and Q I , the submatrix of Q = E(E T E)−1 E T , where E is the matrix of ordinary residuals. Two classes of measures are considered: f(·)tr[H I Q I (I − H I − Q I ) a (I − H I… 
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References

SHOWING 1-10 OF 11 REFERENCES
Characterizations of an Empirical Influence Function for Detecting Influential Cases in Regression
Traditionally, most of the effort in fitting full rank linear regression models has centered on the study of the presence, strength and form of relationships between the measured variables. As is now…
INFLUENCE FUNCTIONS AND REGRESSION DIAGNOSTICS
Detection of influential observations in multivariate regression
Several methods have been suggested, in the literature, to detect influential observations from the data fitting usual linear model y=X∗∗∗+∗∗∗, ∗∗∗∽N(0, ∗∗∗2I). Recently, Chatterjee & Hadi (1986)…
Influential Observations in Linear Regression
Abstract Characteristics of observations which cause them to be influential in a least squares analysis are investigated and related to residual variances, residual correlations, and the convex hull…
A simple graphic for assessing influence in regression G
The leverage-residual plot (L–R plot) is a graphical display of the leverage and residual values for each case in a regression which facilitates the examination of the relative influences of cases…
Influential Observations, High Leverage Points, and Outliers in Linear Regression
A bewilderingly large number of statistical quantities have been proposed to study outliers and influence of individual observations in regression analysis. In this article we describe the…
Sensitivity analysis in linear regression
The Prediction Matrix Role of Variables in a Regression Equation Effects of an Observation on a Regression Equation Assessing the Influence of Multiple Observations Joint Impact of a Variable and an…
Assessment of Local Influence
SUMMARY Statistical models usually involve some degree of approximation and therefore are nearly always wrong. Because of this inexactness, an assessment of the influence of minor perturbations of…
Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
TLDR
This chapter discusses Detecting Influential Observations and Outliers, a method for assessing Collinearity, and its applications in medicine and science.
Finding the Outliers that Matter
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