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I have 5 more less correlated variables measuring conceptually same thing - size. For example, height, weight, shoe size, jacket size and age. I just want to summarize the information from all variables into one and use that single (synthetic) variable in further analysis.

What are the options for doing that?

One of the requirements is to be able to Measure and "tweak" weights of each of the components of the synthetic variable based on exPert judgement... lats say the requirement may be to increase weight of shoe size from 11.34% to 20%. Or reduce weight of another variable because of known measuremen error or some other valid reason.

Any ideas?

user333
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  • I think it is something to do with factor analysis when one latent (unobserved) factor aims to describe the size (it is even a textbook example on such a thing), but I am a bit sleepy to be more concrete right now. – Dmitrij Celov Jul 07 '11 at 23:58
  • A little theoretical knowledge might advance your situation more than any panel of experts. For starters, one would expect the cube root of weight to have a more linear relationship with height, shoe size, and jacket size, which is important information. Standard growth charts could be used to linearize the relationships between age and the other variables. Once approximate linear relationships are established, you can apply the suggestions provided by @Dmitrij or @Mike Lawrence, probably to good effect. – whuber Jul 08 '11 at 04:13
  • Can you please give us mOre details on how to linearize relationshiip? An example would be great. Tnx – user333 Jul 08 '11 at 06:37
  • I hear what you are saying re experts... But... That's a requirement. Things like known data quality (unvalidated figures) can be a valid reason to override .. Say .. PCA weights - how to do that with minimum damage - thats the question! – user333 Jul 08 '11 at 07:20

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Have you looked at PCA? One approach would be to pass your data through PCA and do your analysis on the first principal component. This doesn't let you differentially weight the different original variables however.

Mike Lawrence
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  • +1. But of course PCA "differentially weights" the variables: that's what the coefficients of the first principal component do! But perhaps you mean "weight" in a different sense? – whuber Jul 08 '11 at 04:14
  • Yeah... But can you override PCA weights without breaking it? – user333 Jul 08 '11 at 06:35