Canonical Correspondence Analysis on non-ecological data

Question

I have two datasets: one with samples (rows) taken at different months of the year and abundances or counts of different types of particles I found (columns), and the other with samples (rows) and the probability of sourcing from a particular area (columns) in counts or percentages (this is based on particle backtracking statistics). I have standarized the counts of particle types (type count/sum of type counts) before computing the CCA analysis in R due to uneven counts across samples.

I want to find whether the composition of particle types per sample are related to a particular source. It seems that Canonical correspondence analysis or Redundancy analysis may give me what I'm looking for. It also resembles data sets of ecological data (i.e. instead of species abundance, the response variables are particle type abundance; instead of environmental factors, the explanatory variables are proportion/counts of sources). However, I've never used any of these on this type of data and I would appreciate some suggestions.

Answer 1

RDA and CCA are asymmetrical analysis techniques: you aren't just seeing if they are related (i.e. correlation) but are more specifically seeing how much/if a significant amount of the variation in Y can be explained in X. If you think the data sets are linearly related, RDA is a good choice (if you don't think they are but still want to use RDA instead of CCA, check out transformation-based RDA). CCA is often used when the response variables are thought to respond to X non-linearly (unimodally in particular). I personally don't use CCA too much because the chi-square distance has some properties I am not too fond of (check out Legendre & Legendre's "Ecologically Meaningful Transformations for the Ordination of Species Data" for more details on this).

As a side note, it sounds like your X samples (particle type compositions) sum to a constant across rows/are technically compositional data. You may want to look into methods from the field of compositional data analysis (CoDa) to appropriately transform such values. One easier solution would be to use the CLR transform on rows of X prior to using in an RDA (though there are many solutions and various pros/cons of each).