PCA and symmetric distribution.

[g.arcuri88]

Hello, I hope you can clarify my doubts.
I'm an Italian student of business administration.
For my thesis I study the application of PCA method for the reduction of the original variables, and my data have skewed distribution.
I have read that the PCA works better when the original data have a symmetric distribution. Alternatively, for asymmetric data I considered the algorithm proposed by Hubert et al 2009 (ROBPCA).
I need to understand though, why PCA works best when the data are symmetrical.
Thanks for any reply.

 

[noetsi]

I know in factor analysis normality is desired but not stressed as much as say regression. Generally normality influences the statistical test and factor analysis does very few of these. As far as I know pca does not use many statistical test either. Similarly, at lest with decent sample sizes, there seems to be less concern with outliers in factor analysis and thus I would guess in PCA.

One thing that can be a problem with factor analysis is if your variables are not interval, say they are likert scale or binary data. Because the correlation matrix factor analysis uses assumes linearity/interval data. It is commonly recomended if you have ordinal or even more binary data to use polychoric/tetronic correlations. I don't know for sure how that effects PCA, but I assume it too uses a Pearson correlation matrix which assumes linearity.