Computing composite score from variables that do not follow a likert scale I am trying to develop a regression-weighted composite score. I have 4 variables a, b, c, d that are not necessarily linearly related that I would like to transform to A, B, C, D such that I can combine linearly by regression weights. So I am looking for a way of performing this transformation (a, b, c, d) --> (A, B, C, D). 
For ex: a, b, c, d may not be linearly related, but A = log2a,B = b, C = exp(c), D = 1/log(d) might be. How do I determine this relation? Can anyone guide me how to do this? I tried plotting scatter plots but they don't seem to convey much useful information. Should I just use the correlation?  
As a realtime example, say I want to combine Reputation score, #gold, #silver and #bronze badges and obtain a composite score.    
 A: It's difficult to show a specific analysis without having a reproducible example or set of equations, but two options that you should consider are: 
(1) Principal components regression: In this case you can use a linear combination (with relevant transformations of the inputs) to extract a principal component that you can use as a score variable in subsequent analyses. 
(2) Polychoric/tetrachoric factor or principal component analysis: In this approach you can create a matrix of tetrachoric or polychoric correlations among the items (assuming that they are all categorical or can be treated as such), and then run a factor or principal components analysis. Using a scree plot and related diagnostics, you can extract a factor or component to use as a score in subsequent analyses.
For option number 1, see the pls package in R; for option number 2, see the psych package in R, especially the fa.poly function. The decision to use either option should depend on your understanding of the inputs (e.g., are they categorical or can they be treated as such? can you adequately transform the variables to linearly model the relationships among the data?).
