VARIANCE INFLATION FACTORSName:
Multi-colinearity results when the columns of X have significant interdependence (i.e., one or more columns of X is close to a linear combination of the other columns). Multi-colinearity can result in numerically unstable estimates of the regression coefficients (small changes in X can result in large changes to the estimated regression coefficients).
Pairwise colinearity can be determined from viewing a correlation matrix of the independent variables. However, correlation matrices will not reveal higher order colinearity.
There are a number of approaches to dealing with multi-colinearity. Some of these include:
Variance inflation factors are one measure that can be used to detect multi-colinearity (condition indices are another).
Variance inflation factors are a scaled version of the multiple correlation coefficient between variable j and the rest of the independent variables. Specifically,
where Rj is the multiple correlation coefficient.
Variance inflation factors are often given as the reciprocal of the above formula. In this case, they are referred to as the tolerances.
If Rj equals zero (i.e., no correlation between Xj and the remaining independent variables), then VIFj equals 1. This is the minimum value. Neter, Wasserman, and Kutner (see Reference below) recommend looking at the largest VIF value. A value greater than 10 is an indiciation of potential multi-colinearity problems. Syntax:
where <mat1> is the design matrix for which the variance inflation factors are to be computed;
<y1> is a vector where the resulting variance inflation factors are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional (and rarely used in this context).
"Efficient Computing of Regression Diagnostics", Velleman and Welsch, American Statistician, November, 1981, Vol. 35, No. 4, pp. 234-242.
DIMENSION 100 COLUMNS SKIP 25 READ HALD647.DAT Y X1 X2 X3 X4 SKIP 0 LET N = SIZE X1 LET X0 = SEQUENCE 1 1 N LET Z = CREATE MATRIX X0 X1 X2 X3 X4 LET V = VARIANCE INFLATION FACTORS Z SET WRITE DECIMALS 2 PRINT VThe following output is generated.
VARIABLES--V 2.41 3.45 1.16 3.59 1.39
Date created: 8/6/2002