ki {multiColl}

Stewart's index

Description

The function returns the index of Stewart of the independent variables in the multiple linear regession model.

Usage

ki(X, dummy = FALSE, pos = NULL)

Arguments

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 X. By default dummy=FALSE.

pos

A numeric vector that indicates the position of the dummy variables, if these exist, in the design matrix X. By default pos=NULL.

Details

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.

Value

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).

Author(s)

R. Salmerón ([e-mail]) and C. García ([e-mail]).

References

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.

See Also

VIF.

Examples

# 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)