Let's say X (= 5) number of independent variables are influencing a dependent variable Y (= 1).
A possible solution could be finding out their extent of influence and order them.
However, what if a user is giving different weights to different independent variables, as per their importance in the given context. How to rank in this situtation?
Look at the increase in the R^2 when adding each one of the 5 variables to the model with the other 4. I mean, you fit Y=f(x1,...,x4) and compute the R^2, then you fit Y=f(x1,...,x5) and you compute the new R^2. This is what x5 brings to the new model.
You do that in turn for every possibility of going from 4 to 5 variables (for example Y=f(x1,x2,x3,x5) to Y=f(x1,...,x5), etc.)
You can use factor analysis to see which one of factors that have real influences and terminate poor ...
If i understand your question correctly you have an 'a priori' peking order of relevance of your Xs in terms of their expected influence on your outcome variable Y in a given context. Then the 'a posteriori' weights will be a combination of the ones you get from estimation and the ones you maintained beforehand. The solution to your problem sounds Bayesian to me.
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