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 hi is the i element of the diagonal of the hat matrix, PL is a measure of how hi changes as a variable is added to the regression model. It is computed as:
where
- j = index of independent variable
- i = index of observation
- Xj· = residuals from regressing Xj against the remaining independent variables
Note that the partial leverage is the leverage of the i point in the partial regression plot for the j 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.
{{cite book}}: CS1 maint: multiple names: authors list (link) - 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.
{{cite book}}: CS1 maint: multiple names: authors list (link) - Paul Velleman; Roy Welsch (November 1981). "Efficient Computing of Regression Diagnostiocs". The American Statistician. 35 (4). American Statistical Association: 234–242. doi:10.2307/2683296. JSTOR 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