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 hi is the ith 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:
![{\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}}}}](../I/6b303758a5d5b3f9ac456e7ff85dc4839118d3e2.svg)
where
- j = index of independent variable
- i = index of observation
- Xj·[j] = residuals from regressing Xj against the remaining independent variables
Note that the partial leverage is the leverage of the ith point in the partial regression plot for the jth 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. American Statistical Association. 35 (4): 234–242. doi:10.2307/2683296. JSTOR 2683296.
External links
- Partial Leverage Plot, Dataplot manual, Statistical Engineering Division, National Institute of Standards and Technology
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