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Posted: **Wed Jan 28, 2015 1:25 am**

Hi everybody !

Why don't we get the same thing for the (centered) variance inflation factor of a given coefficient
1/ when we use the ready to use VARINF instruction
2/ when we compute this (centered) variance inflation factor "by hand" according to the help content : "The centered VIF is the ratio of the variance of the coefficient estimate from the original equation divided by the variance from a coefficient estimate from an equation with only that regressor and a constant".

e.g. the following code :

Code: Select all


create u 100
genr x2 = @runif(1,100)
genr x3 = x2 + nrnd
genr x4 = X2 + X3 + nrnd
genr y = 1 + X2 + X3 + X4 + 100 * nrnd
equation eq1.ls y c x2 x3 x4
equation eq2.ls y c x2
scalar vif2 = (eq1.@stderrs(2)^2) / (eq2.@stderrs(2)^2)
eq1.varinf
show vif2

Posted: **Wed Jan 28, 2015 6:48 am**

The manual isn't quite right in the description, since the calculations hold sigmasq constant between the two regressions. The centered VIF is actually the variance of the coefficient from the original regression, divided by sigmasq (from original regression) / inner_product(Xi - mean(xi)).

As an example, you can run the following program that calculates it manually:

Code: Select all


create u 100
genr x2 = @runif(1,100)
genr x3 = x2 + nrnd
genr x4 = X2 + X3 + nrnd
genr y = 1 + X2 + X3 + X4 + 100 * nrnd
equation eq1.ls y c x2 x3 x4
equation eq2.ls y c x2
scalar vif2 = eq1.@coefcov(2,2) / (eq1.@se^2 / @inner(x2-@mean(X2)))
eq1.varinf
show vif2

Posted: **Wed Jan 28, 2015 10:44 am**

all is clear now !!! Thanks a lot !

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