I have performed a PCA to a dinamyc data. This data does not follow a normal distribution. Even when I tried non-linear transformations like logarithmic or square root. Even though results from PCA seem to be logical.
Normality assumption allows to impose confidence limits on the eigenvalues, but this assumption is not an essential condition to be satisfied in PCA analysis , PCA aims at studying interrelationships among a set of study variables and thereby, in some situations can imply dimensionality reduction, particularly for a highly ellipsoid type of data distribution. In my opinion you can go with reporting of your PCA analysis based on total variation and contribution to it by the individual PCs, construction of scree plot to see where the elbow lies to decide on no. of PCs to be retained, and reporting of the factor loadings associated with the study variables i and jth PCs.
Fundamentally PCA is just a change of basis (specifically rotation into a new orthogonal basis) so there is no assumption about normality to worry about.
The new basis is chosen based on maximising the variance of each component in turn, so like any variance based method it is affected by outliers. If you think this is the case you can check by removing extreme outliers and repeating the PCA to see how it changes.
It's also worth mentioning that the major limitation of PCA is that the PCs are always orthogonal.
If your data has structure that's not being well captured by PCA you could consider a non-orthogonal decomposition like Independent Components Analysis.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Techniques
- Meta-Analysis