Hi,
I have come across a problem in which I have to use proportions ( adds to 1) as one of the independent variables in linear regression. It is known that compositional variables are purely multicollinear in nature. Hence I removed one of the variable from compositional data. Still, I find that the coefficients of the compositional variables change drastically by the addition of other predictor variables. I tried PLS regression, and found that the coefficents obtained are logical for all the variables including compositional data. Am I correct by proceeding with PLS regression?
welcome to the field of compositional data analysis. You may transform your proportions using an isometric log-ratio transformation, then do the PLS. If it is only for predicitons used, it may be fine then. If you need proper variance estimates from your coefficient, it might not as simple. For the isometric log-ratio transformation, you may have a look at the R packages robCompositions (function IsomLR()) or compositions (function ilr()). Hope this helps.
Apparently, you are going correctly. It will be better if you carefully study the residual structure to know the validity of PLS assumptions. Use transformation theory if some of the assumptions are violated. I hope this will help.
welcome to the field of compositional data analysis. You may transform your proportions using an isometric log-ratio transformation, then do the PLS. If it is only for predicitons used, it may be fine then. If you need proper variance estimates from your coefficient, it might not as simple. For the isometric log-ratio transformation, you may have a look at the R packages robCompositions (function IsomLR()) or compositions (function ilr()). Hope this helps.
I once tried log ratio transformations (as proposed by Aitchison). I then ran linear regression, but was not satisfied with the results. May be now I must try PLS after transformation.
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