High VIF in constrained design space<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />Hi there,
I'm working on analyzing a design space that is constrained. There are 3 factors, all between 0 and 1, whose sum should not exceed 1. Note that this is not a mixture design, as the sum may be less than 1 but not above.
I've created a design space with 20 experiments. As the outcome of experiments comes from a lengthy CFD computation, there are no replicates (replicates would give exactly the same answer).
I am able to fit a nice quadratic model on the data, but I find Variable Inflation Factors (VIF) values that are very high, from 7 to the low hundreds. My textbooks advise me that these should never exceed 5-10, so I'm a bit worried about this.
I have a suspicion that the high VIF's are caused by the constraint on the design space, because in unconstrained design spaces for similar problems I don't find such high VIF values.
Any thoughts on why the VIF's are so high? is it indeed due to the constraint? I've attached some example data FYI.
High VIF in constrained design spaceYes, sorry, my mistake about the ranges.
Re: High VIF in constrained design spaceIt figures that adding a constraint like 0 <= A+B+C <= 1 will make the design space much less orthogonal therefore increasing VIF's.
Just one thing: you say that the data range is 0 to 0.667, but it clearly is 0 to 1. Entries 2-4 have a value of 1 for each of the three factors.
Re: High VIF in constrained design spaceCertainly applying constraints may induce some collinearity which could manifest itself as high VIF values. However, when I took a look at your data and fitted a response surface the VIF values were all below 10 - see screen shot below:
So the question is why the difference? The data from the DOE will have column properties e.g. Coding ... I am wondering if somewhere along the line these have got mis-specified causing an artificial collinearity due to strange ranges on the coding property?
I've just changed the coding of the A,B,C columns to have ranges 0 tol 1 and now I see the following much higher values of VIF:
My interpretation is that this is being artificially induced by the coding property. If all my factors are in the same numerical range then I am happy to just remove the coding. Alternatively you could specify the coding to be based on the actual data range 0 to 0.667 which brings the values below the "10 threshold".
To understand the nature of the collinearity you can look at the correlations of A,B,C under Multivariate Methods>Multivariate and also within Fit Model: Estimates>Correlation of Estimates.
Dave
