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Interpreting proportions that sum to one as independent variables in linear regression

  • 1.  RE: Interpreting proportions that sum to one as independent variables in linear regression

    Posted 12-31-2015 09:35

    Have you looked at using a Mixture Model? 

    In an advanced Design of Experiments course, you usually cover a type of design called a Mixture Design. In this type of design is usually used by chemical engineers working on the "optimal blend" of something where there is a fixed volume or fixed mass. (When I did my toxicology study, I looked at 100% dose for 11 different chemicals.) You'll have to use R, SAS, Design Expert, JMP or Minitab for the analysis. SPSS and STATA do not have the capability to analyze mixture designs. They will default to a "slack model", where one of the variables will be dropped and the other variables go into a multiple regression analysis. With the mixture models, there will be a high VIF for the terms. Since you can't do anything about them, you ignore them. Good software already knows how to handle such analysis. 

    Once you have your mixture model, you can go back and make predictions and optimize it, if you want to. 

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    Andrew Ekstrom



  • 2.  RE: Interpreting proportions that sum to one as independent variables in linear regression

    Posted 01-01-2016 19:30

    John Aitchison wrote a book, The Statistical Analysis of Compositional Data, that addresses this problem.  Basically you take any one of the variables in the composition and use it as the denominator of log(variable i/ variable baseline) and proceed from there.  

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    Thomas Davan
    Reliability Engineer
    Pratt & Whitney