Re: Principal Components and Repeated Measures

Brian Gaines (
Fri, 8 Jan 1999 22:41:10 -0700

Peter, since your replicated variables are still variables it would be
appropriate to regard your data as a 100 samples of 12 (3x4) variables and
carry out PCA in 12 dimensions.

If your replications are expected to result in similar values then you
would expect to have each set of 4 highly correlated so that the dimesions
will appear as closely aligned.

The PCA analysis is 'valid' in the sense that all the variables are
replicated the same number of times so they will have the same weight in
the analysis (if your replications gave identical results it would make no
difference to the components found how many times they were replicated).

You do not say anything about what the data represents or what you want to
get out of the analysis so it is difficult to comment further. Hopefully,
the above answers the question you posed.

It is important to remember with PCA that what you are doing is rotating
your data in n-dimensional space in such a way as to spread it out
maximally. It is a convenient visual way of plotting the data and showing


>I have a question. Assume you have a dataset nxp with multiple observations
>from the same subject. So if I have 3 variables on 100 subjects measured 4
>times, then my data matrix is 400x3. Does principal components assume that
>each row is an independent observation? If I run a PC on the data set will
>the principal components still be valid. I would greatly appreciate any
>help you may offer in this matter. Thanks.
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