Constrained Optimization

[BillJones]

Hello Everyone,

I'm trying to optimize the following procedure:

1. Select weights and compute the weighted average of 7 factors

2. Rank order the weighted average factors from smallest to largest

3. Bin the weighted average factors into n bins (small to large) with equal weight

4. Examine the relationship of the average values in each bin to another variable (y)

I would like to select the weights in step 1 such that I get:

1. A monotonically increasing relationship between the average values in the bins to the other variable (y)

2. A fairly linear relationship with a line with the steepest slope

My apologies if this type of problem has already been discussed.  I did some searches but couldn't find anything directly related.

Can I use a constrained linear regression where the coefficients are non-negative and sum to 1?  Or would the solution involve some sort of tree procedure?

Thanks very much for any help or  suggestions.

-Bill

[ballardw]

I think you might want to post some example data, dummy is okay, and what the results of what you are asking for from that data as your requirements are not really clear to an outsider.

For example:

Select weights 

Rules or restriction to selecting weights, how many variables may be involved, if more  than one how are the weights applied to the "7 factors"

I would like to select the weights in step 1 such that I get:
1. A monotonically increasing relationship between the average values in the bins to the other variable 

Since you imply that the bins are created after the weights are applied to the factors it is going to be quite a challenge to select the weights to compute the weighted average of he 7 factors.

[BillJones · Accepted solution]

ballardw,

Thanks very much for your response.

My colleague and I came up with a brute force solution.  Basically, we create a data set with all the possible combinations of the weights where they sum to 1.  We then compute the weighted average of the factors, rank, bin into 10 groups with equal size, and run a linear regression.  The output is stored in a file and we'll simply look for the combination of weights that give: monotonic progression (in the dependent variable), steepest slope, and highest coefficient of determination.

Regards,

Bill