I am working on an analysis where I am trying to predict BMI with a subset of microbiota data. Microbiota data is inherently compositional. I will be using a multilevel linear model. For the analysis, I have selected (based on theoretical considerations) certain types of bacteria (SCFA producers) that should be associated with BMI. Preferably, this would result in one sum variable that represents these bacteria. However, I have been struggling to find an adequate solution or approach for this setup. I am not a microbiota or compositional data expert. I'm more trained in frequentist statistical methods.
I have read into multiple different options such as using a CLR (centered log-ratio) and ILR (isometric log-ratio) transformations. The initial idea was to use a CLR transformation and simply add up the transformed values of my picked bacteria. However, after further consideration, I am highly doubting whether this is statistically sound.
The other idea was to use the ILR transformation. Here I would make two sum variables of both the abundances of my picked bacteria (SCFA producers) and the abundances of all other bacteria in my sample. I would then calculate a 'balance' between these two groups with the ILR transformation. From what I have read this seems like a better approach, however, I am not certain about this. I have not come across any cases, in books or articles, where 'balances' are calculated over hand-picked, theory-driven and maybe arbitrary groups.
Any thoughts or comments on this issue would be highly appreciated.