Partial leverage explained

In regression analysis, partial leverage (PL) is a measure of the contribution of the individual independent variables to the total leverage of each observation. That is, if h_i is the i^th element of the diagonal of the hat matrix, PL is a measure of how h_i changes as a variable is added to the regression model. It is computed as:

\left( PL _{j\right)} _{i} = (\left(X _{j\bullet[j]} \right) ^{2} _{i})/(\sum ^{n\left(X} _{j\bullet[j]} \right) ^{2} _{k})

where

j = index of independent variable

i = index of observation

X_j·[''j''] = residuals from regressing X_j against the remaining independent variables

Note that the partial leverage is the leverage of the i^th point in the partial regression plot for the j^th variable. Data points with large partial leverage for an independent variable can exert undue influence on the selection of that variable in automatic regression model building procedures.

See also

• Leverage
• Partial residual plot
• Partial regression plot
• Variance inflation factor for a multi-linear fit

References

• Book: Modern Regression Methods. Tom Ryan. John Wiley. 1997.
• Book: Applied Linear Statistical Models. 3rd. Neter, Wasserman, and Kunter. 1990. Irwin.
• Book: Applied Regression Analysis. 3rd. Draper and Smith. John Wiley. 1998.
• Book: Residuals and Influence in Regression. Cook and Weisberg. Chapman and Hall. 1982.
• Book: Regression Diagnostics. Belsley, Kuh, and Welsch. John Wiley. 1980.
• Efficient Computing of Regression Diagnostiocs. Paul Velleman. Roy Welsch. The American Statistician. November 1981. 35. 234–242. 10.2307/2683296. 4. American Statistical Association. 2683296.

External links

• Partial Leverage Plot, Dataplot manual, Statistical Engineering Division, National Institute of Standards and Technology