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Change from VIF in Evaluate Design

Phil_Kay

Hi,

A customer wants some information on why the Evaluate Design report no longer gives VIFs but instead has Fractional Increase in CI Length. Is this a JMP innovation or is there an external reference that I can cite? My explanation was that it is a more practical measure.

Thanks,

Phil

Accepted answers

stan_koprowski

Hi Phil,

I exchanged emails with Brad and he asked me to post the following response because he was not able to login at this time.

Stan

The VIF is not scale invariant. So, different dummy variable choices for categorical factors can lead to different values of the VIF for the same design. The standard definition of VIF uses the R^2 value for the regression of a given term on the other terms in a model. The Custom Designer used a different definition based on the value of the diagonal elements of the inverse of X'X. For two-level screening designs coded -1 to 1, the diagonal elements of the inverse of X'X for an orthogonal design are 1/n. A design that is not orthogonal will have diagonal elements that are larger than 1/n. So, if you multiply this element by n you get how much bigger the variance got - the variance inflation if you will. These two definitions are equivalent for two-level screening designs with factors coded -1 to 1.

The Fit Model VIF uses effects coding for categorical factors. The Custom Designer uses an orthogonal coding for categorical factors. If you put the 3x3 factorial design into Fit Model, you see that the VIF is not 1 even though the design is orthogonal. That is because effects coding is not an orthogonal coding. Given these unavoidable differences it seemed necessary to calculate something that gave the same kind of information as VIF but try to make it more practical. The estimation efficiency does this.

All comments

DonMcCormack

I can't say why Brad might have changed this, but I find fractional increase in CI a much more meaningful and useable quantity than VIF.

Bill_Worley

One of the reasons I heard that prompted the change was the VIF in the standard least squares report under parameter estimates and the VIF in the Design Evaluation were giving different values, and at times were so different that it was causing confusion for folks.

Phil_Kay

Hi Bill,

That rings a bell. I can’t remember where I heard/read about it though. I’ve just checked and we do get different VIFs in the fit model report.

The customer would like to know why the VIFs are different from those they calculate in Design Expert. I guess this is a related issue.

Thanks,

Phil

stan_koprowski

Hi Phil,

I exchanged emails with Brad and he asked me to post the following response because he was not able to login at this time.

Stan

Phil_Kay

Thanks Stan and Brad,

I'll send on this explanation to the customer.

One more thing: The customer wants to know how big the VIF in the Custom Designer in JMP10 can be before it should be a concern. "How long is a piece of string" might be my answer.

They have created a 16 run custom design, 3 factors, RSM model with a constraint. The VIFs range from 2 to 10 (one of the quadratic effects). I guess they are concerned about a VIF of 10. The corresponding fractional increase in CI length for that effect is 2.224. The VIF that Design Expert reports is 2.19.

Bill_Worley

Hi Phil,

Has your customer looked at the factors with the multivariate platform? That might be a good way to determine the extent of the correlation between the factors of concern.

As for the VIF value, in a previous life we would recommend that anything above 3 should be investigated further.

Regards,

Bill