Risk Model Re-Weighting Help Needed

#1
Long story somewhat short … My company uses a risk model with 10+ variables. Each of these variables is weighted according to the risk it theoretically poses to the business. I have been tasked with re-weighting the variables and I would prefer to do so in some sort of statistically sound manner. My basic idea was to take the raw scores, which have been produced by this model, and attempt to determine which of the variables are driving the composite score and weight those heavier. I am somewhat statistically savvy, but I have not figured out how to get this done. My initial thought was to do a multiple regression, but since what I have is a dependent variable (the composite score) and a bunch of independent variables adding up to equal it, the coefficients will always be 1.

Any help would be GREATLY appreciated. Thanks.
 
#2
Ok, allow me to re-frame ...

Perhaps my original question was too convoluted. What I am essentially trying to do is determine the relative power each variable has so I can assign weights to each variable. The weights are currently assigned by gut instinct and I think there must be a better way.

I simulated this with test data and I am hoping someone out there can tell me if this theory holds water ... 2 variables with the same average value across a set of data, 1 variable has a high standard deviation, the other has a much lower standard deviation--my theory is that a variable with a lower SD will influence the dependent variable less, overall, and is therefore weaker in terms of influencing the final outcome. What I did was take the SD of 5 fictitious variables divided by the average of each of the variables. I then divided these values by the TOTAL (which adds up to 100%) to weight them.

I'd be very appreciative if someone could comment on this. Thanks!
 

Axl

New Member
#3
I simulated this with test data and I am hoping someone out there can tell me if this theory holds water ... 2 variables with the same average value across a set of data, 1 variable has a high standard deviation, the other has a much lower standard deviation--my theory is that a variable with a lower SD will influence the dependent variable less, overall, and is therefore weaker in terms of influencing the final outcome. What I did was take the SD of 5 fictitious variables divided by the average of each of the variables. I then divided these values by the TOTAL (which adds up to 100%) to weight them.
What software is being used to perform the analysis? Are the correlations linear? If not done so already, the data should be normalized first. Then the weights when calculated will clearly tell which columns are weighted more and which columns are weighted less. Note you also have to have enough data. For 10 variables I normally have 100,000+ rows of data. Maybe someone else will chime in with a better rule of thumb for this. Finally the method of using standard deviation to weight columns most likely won't work. This can be tested by measuring the correlation of standard deviation weighted values versus the correlation of linear regression weighted values. I think you'll find that the linear regression model will have higher correlation with the dependent variable.

HTH.