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Leverage is also related to the i-th observation's [:FAQ/mahal:Mahalanobis distance], $$\mbox{MD}_text{i}$$, such that for sample size, N Leverage for observation i = (MD/(N-1)) + (1/N) so Critical $$\mbox{MD}_text{i}$$ = ($$\frac{\mbox{2(p+1)}}{\mbox{N}} - \frac{1}{\mbox{N}})(\mbox{N-1}) (See Tabachnick and Fidell) |
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| '''Hair, J., Anderson, R., and Tatham, R. (1992).''' Multivariate Data Analysis (third edition). Englewood Cliffs, NJ: Prentice-Hall. | '''Hair, J., Anderson, R., Tatham, R. and Black W. (1998).''' Multivariate Data Analysis (fifth edition). Englewood Cliffs, NJ: Prentice-Hall. |
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Checking for outliers in regression
According to Hoaglin and Welsch (1978) leverage values above 2(p+1)/n where p predictors are in the regression on n observations (items) are influential values. If the sample size is < 30 a stiffer criterion such as 3(p+1)/n is suggested.
Leverage is also related to the i-th observation's [:FAQ/mahal:Mahalanobis distance], $$\mbox{MD}_text{i}$$, such that for sample size, N
Leverage for observation i = (MD/(N-1)) + (1/N)
so
Critical $$\mbox{MD}_text{i}$$ = ($$\frac{\mbox{2(p+1)}}{\mbox{N}} - \frac{1}{\mbox{N}})(\mbox{N-1})
(See Tabachnick and Fidell)
Hair, Anderson, Tatham and Black (1998) suggest Cook's distances greater than 1 are influential.
References
Hair, J., Anderson, R., Tatham, R. and Black W. (1998). Multivariate Data Analysis (fifth edition). Englewood Cliffs, NJ: Prentice-Hall.
Hoaglin, D. C. and Welsch, R. E. (1978). The hat matrix in regression and ANOVA. The American Statistician 32, 17-22.
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