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I have a dataset with 1000 individuals who each came in for a minimum of 1 to a maximum of 10 visits during which we measured their arm strength in various directions (forward, back, sideways etc.). I would like to do PCA to combine these various directions (10) into a single variable.

My question is should I use the measurements from all the visits or perhaps just the baseline visit when doing the PCA? I am worried that using the measurements from all visits may bias the PCA results in favor of individuals who had more visits.

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  • $\begingroup$ If you only have three directions to begin with, why is it necessary to reduce it to one? Whether the results are useful really depends on what you're going to use this for, so perhaps you could elaborate on why dimension reduction is required in the first place. $\endgroup$ May 21 at 14:09
  • $\begingroup$ I was oversimplifying my data- in reality I have maybe 10 variables I would like to condense to 1-2 PC's. I am doing this because I will then run regressions and I would like to limit multiple testing. $\endgroup$
    – Hank Lin
    May 21 at 14:12
  • $\begingroup$ You have a thousand individuals, surely any practically relevant effect would survive a multiple testing correction for 10 or so tests? $\endgroup$ May 21 at 14:15
  • $\begingroup$ It's really closer to 100 tests as there are multiple relationships we are examining for each. I guess I am more confused about the nature of PCA and how it is affected by this "multilevel" data structure. $\endgroup$
    – Hank Lin
    May 21 at 14:26
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I think what I would do is run PCA both ways, or even three ways:

  • Just use the first visit of each person
  • Average each person's visits into a single entry
  • Use all data

And then compare the results from each approach. If the numbers come out roughly the same, allowing you to draw the same conclusions, then it didn't matter.

But if they differ it forces you to learn something interesting about the data. Are the people who did more visits qualitatively different in some way? (E.g. competitive sporty types who decided they were going to go away and train for the arm strength direction they were worst at, then come back and be tested again.)

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