NMDS or PCA are usually employed for visualization of a (complex) beta diversity matrix. However, PCA try to maximize variation in several "ORTHOGONAL" axes (they should be independent between them).
When a factor has several groups, PCO (e.g. samples from 17 different environments) is not able to separate into the same number of clusters (even when statistics have a strong effect and high correlation).
Is there a way to visualize those complex data? Residuals? Discriminant Analyses?
Thanks
Hi Juan,
To answer this question efficiently I think a bit more information is needed. What kind of data do you have (dependent and independent variables) and what is the question you would like to address? In addition, in what way do you think your data is complex?
NMDS, PCA, PCO, CA etc are all computationally different methods of doing the same thing, namely summarizing main patterns in multivariate data in a few axes. Clustering and discriminant analyse have a slightly different objective in that they try to group objects in discrete groups - and disciminant analysis tries to find the best predictors for a priori group membership.
Cheers,
Jasper
Hi Jasper,
I am completely agree with your explanations. Muy question was more phylosofical.
PCA should generate orthogonal axes (by definition) and any set of data should generate a shotgun (in 2D or 3D, or any set of axes). However, most of the figures in published papers show two-three clear clusters or a gradient between PC1, PC2 and a third variable (some of my studies reproduce this pattern). Moreover, I have the suspect that PCA have problems for visualizations of more than 3 cluster (more or less, one cluster per axis).
One of my problematic studies is about bacterial communities from 17 bird species. Any statistical test shows me a highly significant p value (but a low correlation coefficient), bacterial communities differ between bird species. When I am trying to visualize these bacterial samples in a PCA (NMDS, diffusion maps...), I only get a shotgun (no cluster at all). That result makes me think that differences in bacterial communities between bird species are not possible to visualize, and then I started to use discriminant or clustering analyses.
Thanks a lot for answering and sorry for mylack of deep knowlegde in mutlivariant analyses.
Why don't you use hierarchical clustering method based on matrix distance (using pairwise distance based on bray-curtis or Jaccard indices)?
Just methodological question: what DNA template did you use to study the bacterial community of the birds? faeces?
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