optimize selection of categories for 2 variables in order to obtain best diagonal

[frozenSea]

Hello.

I have the following problem that I need to solve.

Let's suppose I have 2 variables (A and B) with 10 categories (ordinal most commonly) each containing nA1,...nA10,nb1,...nb10 clients each. I want to regroup these 10 categories into 3 categories called 1A, 1B and 1C (and for B:2A, 2B and 2C) and create a new variable lets say NEW_A and NEW_B.

Now, the problem is to tell SAS to optimize the selection of these new subcategories of A in order to maximize the diagonal of NEW_A and NEW_B, so the selection of -let's suppose 1A- NEW_A will bring the most clients of 2A, 1B of 2B...etc.

So the selection need to be recursive. That's all I could figure so far and the key is to maximize number of clients.

All help is greatly appreciated.

Thanks!

Jay

[rayIII]

Hi, Jay. I've been thinking about how to approach this problem. To find the optimal groupings there are many combinations to consider but you could try this simple (but nonexhaustive) approach: 

a. Build a decision tree to predict B from A using maxbranches = 3 and maxdepth = 1. This will give you A' which has grouped the 10 original categories into 3. 

b. Now predict A' from B, agaiin using maxbranches =3 and maxdepth = 1. This gives you B', with three ordered categories. 

Examine the 3 by 3 crosstabulation between A' and B'.

You can get the code for mapping A to A' and B to B' from the Decision Tree node in Enterprise Miner and apply the code using as SAS Code node. 

If that doesn't give you a satisfactory solution, try posting your question to the SAS “Mathematical Optimization, Discrete-event Simulation, and OR” community.  

Hope this helps.

Ray