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I want to build an index from, say, 13 variables. I run a PCA for these 13 variables to produce 13 principal components, 5 of which have an Eigenvalue of more than 1. While some researchers use only the first principal component as their index, this does not seem advisable here since PC1 only has a proportion of variance explained of 23%. So, does it make sense to sum PC = PC1 + PC2 + ... + PC5 as my index?

amoeba
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user6717281
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    http://stats.stackexchange.com/q/133492/3277 is the duplicate. Answered basically in comments there. – ttnphns Sep 25 '16 at 09:21
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    @ttnphns (+1) ...and the answer is no. – amoeba Sep 25 '16 at 15:05
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    @ttnphns thanks. Noted in your previous answer that you are mainly concerned with the assumption that the PCs are orthogonal and hence not substitutes for one another (as implied by your adding oranges and apples analogy). What about using a Cobb-Douglas form: new index = (PC1)^x1*(PC2)^x2 etc. where x1, x2 ... are the proportion of variance explained by that PC as a fraction of total variance explained by all PCs retained? Would that address the problem of imperfect substitutes? – user6717281 Sep 26 '16 at 03:50
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    (PC1)^x1*(PC2)^x2 Looks reasonable. That formula can make sense. At least from the first glance. I haven't used it so can't say for sure. You have to think what to do with the problem of sign of each PC's value. The formula is feasible only for positive PC values. – ttnphns Sep 26 '16 at 07:23

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