In one of the thesis defense seminars, one of the professors argued that the statement “Principal Coordinates Analysis (PCoA) of bray Curtis distances showed that the first two principal coordinates were able to explain 42.2%” is inaccurate and it is completely useless. He further argued that in PCoA, axis value percentages have no meaning to it and it doesn't explain anything.
I am wondering if this is true. I have seen hundreds of research articles stating the same in describing their PCoA. Could someone please guide me to a good write up explaining this or, explain why its true fro PCA but not for PCoA?
This is how I understood it back when I learned it:
PCA % –> how much of the raw data variance is explained by each axis
PCoA % –> how much of the distance matrix variation is explained by each axis
I’m not an expert in the matter, but I’m almost sure that if you use non-Euclidean distances (like Bray-Curtis) you can get negative eigenvalues, so those percentages are an approximation (and maybe that’s why your professor said that the percentages are inaccurate).
I’m not a statistician myself, but their suggestion to use Shepard plots for PCoA seems plausible. I’m experimenting with using them alongside ordination plots (example below) and it can really tell more about the captured variance from raw data, and not just the distance matrices.
