If you're going to do a PCA then the typical approach would be to standardize them first. Use of PCA requires no assumptions about the variable distributions. I wonder how much variance a single component will explain in those variables. As someone who teaches multivariate a lot, I'd actually be curious to hear if you're so inclined. If so, you could email me at robert.pearson@gvsu.edu.
Bob
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Robert Pearson
Asst. Professor
Grand Valley State University
Original Message:
Sent: 01-26-2016 09:16
From: Debra Stiver
Subject: Creating Vector Scores
When combining multiple data vectors, each with different units and levels of variation, into a single composite vector, can Z-scores be used to to standardize each vector even if the underlying data are of different distributions? For example: Creating a vector of economic scores for US metropolitan areas by combining GDP per capita, employment rate, and cost of living index into a single average "score" for the purpose of ranking the metropolitan areas by that composite score vector. GDP per capita, employment rate, and cost of living index are all of different units, variation and distributions, but to give an overall score to a metropolitan area based on all three would require them to be standardized. Will Z-scores be valid and comparable across these and other measures, or would a different method of standardization accomplish this?