How to relate isometric log ratio [ILR] transformed compositional data to original attributes?

[mortonjt (Jamie Morton)]

1. Have you been able to run the gneiss tutorial?

There are also a few similar posts on how to interpret balances, which may help with figuring out how to interpret these results

Understanding Gneiss - questions regarding the analysis

Sorry I meant this type of heatmap, not the one in the regression .qzv: [image]

Gneiss: Coordinates from the balances vs. metadata plot

Hi everybody and @mortonjt Two things from my gneiss analysis that I would love to have your input on. 1. I wanted to check if I take the right approach in testing my hypothesis and plugging in the right meta-variable in the appropriate command. Basically, I am seeing variation in the microbial community along a soil depth profile and I would like to check several geochemical parameters as metadata if there is some correlation using balances. So, I chose gradient-clustering because I want to a…

Balance interpretation confusion

Hi @mortonjt, Yes, I mean that I have multiple levels within a variable, I have treatment (drug 1 vs drug 2) and Day (day 0 vs day 14). I would like to visualize the effects of the different treatments across the different time points. Thanks, I will try the lme-regression, as treatment over time is a question we are curious about. I saw that I could look at the balance-taxonomy, but I will definitely look into pulling out the best balances and plotting them remotely. Thanks, Samantha

2. You end up with m-1 attributes since we are dealing with proportions, which live in a m-1 dimensional space. The ilr is a direct mapping from the m-simplex to m-1 real space.

Another way to think of it is the ilr transform computes the transformation between the proportions in the tips and log ratios in the ancestral states in the tree. If there are m tips, there are exactly m-1 internal nodes.

3. No. The ilr tranform will not give pairwise correlations, that is a very different discussion. I would look at tools such as SPEIC-EASI to answer those sorts of questions

4. If I am understanding this question correctly, the answer is yes.
   Each balance just represents two groups of features (in the context of phylogenetics, you can think of a balance as an ancestral state in the phylogenetic tree.)