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I am currently creating a multiple variable index and tried using Principal Components Analysis to determine the weight of each variable. Specifically I'm using the prcomp function in R and squaring the loadings of the first component to determine the weights. In the past only one component explained enough of the variance but for my present use case I would need to keep 3 or 4.

The ultimate goal for the weighted index is to serve as a single variable that can be used to classify products into different groups. Cluster analysis is not possible in this case or any other complex statistical function to form the groups. As a result I plan to base the groups on percentiles of my weighted index. The answer to this question (Creating a single index from several principal components or factors retained from PCA/FA) suggest any type of combining of multiple components is probably not a good idea. What are some good alternatives to PCA I could use to arrive at my weights?

te time
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Howard Wainer (1976) spoke for many when he recommended unit weights vs regression weights. You could just sum things up, or sum up normalized values, if scales differ substantially. Particularly, if sample size is not large, you will likely find that, out-of-sample, unit weights match or outperform regression weights. I understand that you don't seem to have a criterion, but I'd bet on unit weights being a not-bad alternative. At least, they carry no sampling variance.

Ed Rigdon
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