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I have some data where I want to predict a continuous, approximately normally distributed response/dependent variable with three predictors which are all proportions (i.e. 0-1). The three proportions sum to 1 per case (i.e. 100%).

So far I have tried correlation which gives easily interpretable results but only takes into account one of the predictors (so one must try all three and choose the best).

I have also tried OLS multiple regression, but since the predictors correlate negatively strongly and are linearly dependent (since they sum to 1), it seems to me that this method is not optimal either. It was not meant for this kind of data. OLS MR also standardizes the values first, which strikes me as not something one would want to do with this kind of data.

I am wondering if there is some method I haven't heard of that is good for this kind of data?

Would the method be able to handle multi-level data too? I have subdivisions for some of the datapoints below and ideally want to model them together with the first 49.

I provide the data below. Some of the response data is missing.

Group1  Group2  Group3  Outcome
0.5 0   0.5  
0.15    0.77    0.08     
0.71    0.04    0.25    421.28
0.04    0.96    0   365.372443
0.16    0.79    0.05    323.644343
0.37    0.25    0.38    333
0.38    0.58    0.04     
0.21    0.01    0.78    400.7
0.71    0.19    0.1 415.88
0.14    0.86    0   414.080918
0.52    0.05    0.43    441.37
0.44    0.17    0.39    406.05
0.49    0.2 0.31    447.7
0.72    0.2 0.08    518.2001788208
0.15    0.77    0.08     
0.5 0.5 0    
0.28    0.56    0.16    321.177442
0.47    0.42    0.12    338.474556858
0.42    0.06    0.52    388.8692334914
0.11    0.89    0    
0.4 0.07    0.53    380.5622669942
0.4 0.6 0    
0   0.77    0.23    344.059538
0.12    0.81    0.07    313.34
0.5 0.08    0.42    378.2281918766
0.04    0.96    0   287.157381
0.11    0.85    0.04    360.042389
0.08    0.86    0.06    287.29
0.18    0.75    0.08    335.489631
0.15    0.77    0.08     
0.42    0.07    0.51    439.08
0.15    0.77    0.08     
0.57    0.2 0.23    374.6937385296
0.25    0.39    0.36    389.74
0.12    0.07    0.81    385.43
0.64    0.21    0.15    374.084946
0.55    0.08    0.37    367.8715419396
0.15    0.1 0.75    351.61
0.4 0.6 0   337.79
0.15    0.77    0.08     
0.09    0.91    0    
0.24    0.63    0.13    437.150625
0.83    0.09    0.08    448.09
0.79    0.14    0.07    516.605766
0.13    0.81    0.07    309.36
0.56    0.19    0.25    431.992418
0.07    0.82    0.11     
0.31    0.64    0.04     
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If there is multicollinearity among the predictors the best way solve this problem is to do ridge regression on this data. I suppose group1-2-3 are the predictors, so you can do analyse in R software. But what do you mean about multi-level data? If you asking high dimension e.g p>n, ridge solution can deal with kind of data too.

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  • $\begingroup$ I explained that in the question: I have subdivisions for some of the datapoints below and ideally want to model them together with the first 49. I haven't heard of ridge regression. I will take a look. $\endgroup$ – Deleet May 29 '15 at 13:56

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