Just a comment on this one, from a pragmatic point of view. It is of course true that PCA is only *guaranteed* to produce components maximizing variance if you have multivariate normality. The theory of PCA is based on this assumption. But in many cases, PCA is used purely as a visualization device, projecting a multivariate data set onto a sheet of paper so we can see it. For visualization of non-normal data, one could play around with different techniques, such as PCA, PCO, NMDS, projection pursuit etc., and then find that PCA does (or does not) perform well for the given data set. There is no law against making any linear combination you want of your variates, if it reveals information. For example, PCA may be perfectly adequate for resolving two well-separated groups, if the within-group variance is relatively small.
Of course, when using PCA for non-normal data one must be a little careful and not over-interpret the results (especially not the component loadings), but I think it's too harsh to dismiss its use totally. I'm sure the hard-liners will flame me to pieces for this email, but I hope they will at least give me credit for my courage :-) Dr. Oyvind Hammer Geological Museum University of Oslo > PCA Analysis assumes multivariate normality. > > Kathleen M. Robinette, Ph.D. > Principal Research Anthropologist > Air Force Research Laboratory == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
