I have been diving deep into compositional data analysis. Here is a great thread containing a conversation with Thomas Quinn, who is pushing this type of research in microbiology, about some intricacies of compositional data analysis . In that thread proportionality is defined but essentially it can be used as a stand-in replacement for correlation that is compositionally valid.
My question is out of scope for that thread so I thought of asking here. I have a compositional dataset
X that is made up of genes as components and samples as compositions. I've made a transformation (that might not be the correct term) where I sum up the counts for different groups of genes. However, a single component sometimes belong to multiple groups so it's not compositional anymore. Furthermore, I normalize by the length of the genes in each group so the data is certainly not compositional.
My question is whether or not I can use the
proportionality rho metric in this case?
Certainly I can use it and get an answer out with propr but would this be valid after I've applied these types of data manipulation?