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:
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.
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.
This article incorporates public domain material from the National Institute of Standards and Technology.
January 26, 2023
partial, leverage, regression, analysis, partial, leverage, measure, contribution, individual, independent, variables, total, leverage, each, observation, that, element, diagonal, matrix, measure, changes, variable, added, regression, model, computed, displays. 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 P L j i X j j i 2 k 1 n X j j k 2 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 where j index of independent variable i index of observation Xj j residuals from regressing Xj against the remaining independent variablesNote 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 EditLeverage Partial residual plot Partial regression plot Variance inflation factor for a multi linear fitReferences EditTom Ryan 1997 Modern Regression Methods John Wiley Neter Wasserman and Kunter 1990 Applied Linear Statistical Models 3rd ed Irwin a href Template Cite book html title Template Cite book cite book a 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 a href Template Cite book html title Template Cite book cite book a 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 EditPartial 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 Retrieved from https en wikipedia org w index php title Partial leverage amp oldid 1042292233, wikipedia, wiki, book, books, library,
