Partial leverage

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:

[math]\displaystyle{ \left(\mathrm{PL}_j\right)_i = \frac{\left(X_{j\bullet[j]}\right)_i^2}{\sum_{k=1}^n\left(X_{j\bullet[j]}\right)_k^2} }[/math]

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

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

External links

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

 This article incorporates public domain material from the National Institute of Standards and Technology website https://www.nist.gov.