Stewart's index
The function returns the index of Stewart of the independent variables in the multiple linear regession model.
ki(X, dummy = FALSE, pos = NULL)
X |
A numeric design matrix that should contain more than one regressor (intercept included). |
dummy |
A logical value that indicates if there are dummy variables in the design matrix |
pos |
A numeric vector that indicates the position of the dummy variables, if these exist, in the design matrix |
The index of Stewart allows to detect the near essential and non-essential multicollinearity existing in a multiple linear regression model. In addition, due to its relation with the Variance Inflation Factor (VIF), it allows to calculate the proportion of essential and non-essential multicollinearity in each independent variable (intercept excluded). The Stewart's index for the intercept indicates the degree of non-essential multicollinearity existing in the model.
The relation of the the VIF with the index of Stewart implies that it should not be calculated for non-quantitative variables.
ki |
Stewart's index for each independent variable. |
porc1 |
Proportion of essential multicollinearity in the i-th independent variable (without intercept). |
porc2 |
Proportion of non-essential multicollinearity in the i-th independent variable (without intercept). |
R. Salmerón (romansg@ugr.es) and C. García (cbgarcia@ugr.es).
G. Stewart (1987). Collinearity and least squares regression. Statistical Science, 2 (1), 68-100.
L. R. Klein and A.S. Goldberger (1964). An economic model of the United States, 1929-1952. North Holland Publishing Company, Amsterdan.
H. Theil (1971). Principles of Econometrics. John Wiley & Sons, New York.
VIF.
# Henri Theil's textile consumption data modified data(theil) head(theil) cte = array(1,length(theil[,2])) theil.X = cbind(cte,theil[,-(1:2)]) ki(theil.X, TRUE, pos = 4) # Klein and Goldberger data on consumption and wage income data(KG) head(KG) cte = array(1,length(KG[,1])) KG.X = cbind(cte,KG[,-1]) ki(KG.X)
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