# Re: Principal Components and Repeated Measures

Richard Bell (rcbell@rubens.its.unimelb.edu.au)
Tue, 12 Jan 1999 10:36:43 +1100

Peter

If you have 3 variables on 4 occasions for 100 subjects, then your data set
is a three-mode data set
100 x 4 x 3.

A standard statistical analysis would model this as 100 x 12 with the 12
'variables' representing two within-subject factors. I suspect this might
be the best way to analyse your data since you will have replicates of your
variables over time in the analysis. You might get a variable and a time
factor. [Who knows?]

Patrick Slater on the other hand advocated the structure you suggest with
his PREFAN analysis although I believe he removed the person means from the
data. But why would you want to do principal components on only three
variables?

Technically individual differences multidimensional scaling could cope with
this as Alexander Winogradov suggests. You would have to choose which mode
you wished to use as weights (persons or occasions) and which of these two
you chose to 'lose' as replications. My intuition would be to use persons
as the replications. You can do this fairly easily in SPSS [I have a
document which shows how to do this and other things with SPSS commands]
although I suspect the algorithm there [ALSCAL] may be a little vulnerable
to the small number of variables. I also have a new program for the
analysis of multiple grids [GRIDSCAL] which should be available in a
quasi-beta form in a couple of weeks which would also handle this kind of
analysis. It also performs a version of three-mode factor analysis which
doesn't involve losing any of the information.

Richard Bell
Dept of Psychology
University of Melbourne

At 09:20 8/01/99 -0600, you wrote:
>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
>

>
>PETER L. BONATE, PhD.
>
>Quintiles
>POB 9627  (F4-M3112)
>Kansas City, MO  64134
>phone:  816-966-3723
>fax:  816-966-6999
>

>

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