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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 = $$\frac{\mbox{MD}_text{i}}{\mbox{N-1}} + \frac{\mbox{1}}{\mbox{N}}$$ so Critical $$\mbox{MD}_text{i} = (\frac{\mbox{2(p+1)}}{\mbox{N}} - \frac{1}{\mbox{N}})(\mbox{N-1}) $$ (See Tabachnick and Fidell) Other outlier detection methods using boxplots are in the Exploratory Data Analysis Graduate talk located [[StatsCourse2009|here]] or by using z-scores using tests such as Grubb's test - further details and an on-line calculator are located [[http://www.graphpad.com/quickcalcs/Grubbs1.cfm|here.]] |
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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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| [wiki:FAQ Return to Statistics FAQ page] | [[FAQ|Return to Statistics FAQ page]] |
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| [wiki:CbuStatistics Return to Statistics main page] | [[CbuStatistics|Return to Statistics main page]] |
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| These pages are maintained by [mailto:ian.nimmo-smith@mrc-cbu.cam.ac.uk Ian Nimmo-Smith] and [mailto:peter.watson@mrc-cbu.cam.ac.uk Peter Watson] |
These pages are maintained by [[mailto:ian.nimmo-smith@mrc-cbu.cam.ac.uk|Ian Nimmo-Smith]] and [[mailto:peter.watson@mrc-cbu.cam.ac.uk|Peter Watson]] |
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 Mahalanobis distance, $$\mbox{MD}_text{i}$$, such that for sample size, N
Leverage for observation i = $$\frac{\mbox{MD}_text{i}}{\mbox{N-1}} + \frac{\mbox{1}}{\mbox{N}}$$
so
Critical $$\mbox{MD}_text{i} = (\frac{\mbox{2(p+1)}}{\mbox{N}} - \frac{1}{\mbox{N}})(\mbox{N-1}) $$
(See Tabachnick and Fidell)
Other outlier detection methods using boxplots are in the Exploratory Data Analysis Graduate talk located here or by using z-scores using tests such as Grubb's test - further details and an on-line calculator are located here.
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.
Return to Statistics main page
These pages are maintained by Ian Nimmo-Smith and Peter Watson