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Suppose that I'm calculating distances of a company branches in every state from main branch of that state. After that I'm combining this feature with other features to creating a composite indicator with different weights (using factor analysis). Distances are based on kilometers. There isn't any problem to calculate branches distances but as you know for main company in every state the distance is 0 so the contribution of this feature to indicator is zero.

Let's see data after normalization (use mean or trimmed mean as denominator of this feature for normalization):

c_1 0.518240612
c_2 0.497028927
c_3 0.437494131
c_4 0.557290719
c_5 0.995532618
c_6 0
c_7 0.24987914
c_8 1.090686096
c_9 1.399784307

Suppose that 0 (main company in above state) has very very low value like 0.000001 and we're comparing this value to c_5 branch normalized distance value (0.995532618) so c_5 is 0.995532618/0.000001=995532.618 times bigger than main capital c_6 in this feature. I think this a problem in our calculation. Is this idea true? What is your idea about changing 0 (main companies in every state) to average of all distances (in all states) and after that normalize data and create composite indicator?

PS. The objective of factor analysis here is to calculate weights of every feature to design composite indicator. We are combining some features to calculate performance of every branch. We are giving higher scores to companies that have higher values of distance because of welfare issues.

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    $\begingroup$ This is a pretty specific methodological question that lacks a specific answer. It would help our understanding if you elaborated a bit more on what you are trying to do with this analysis, e.g., why would you want to do a factor analysis of this data in the first place? What is the objective in creating a composite indicator? $\endgroup$ – Mike Hunter Nov 20 '15 at 13:01
  • $\begingroup$ @DJohnson. Thank you for answer. Question was edited. $\endgroup$ – user2991243 Nov 20 '15 at 13:09

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