Analysis of a dataset including dichotomial, ordinal and % data

Question

I'm working on a dataset which is giving me trouble. I have 200 samples (Sample 1, Sample 2...). An example dataset (limited to 15 samples) is here. My dataset is structured with the following columns (I'll try to simplify):

1. Sample source. Type of data: dichotomic. It can be SEDIMENT or WATER.
2. Sequencing technique. 4 categories: A,B,C,D (non numeric values)
3. Salinity. 3 categories: salt, brackish, freshwater
4. Depth. 5 categories: surface, epi, meso, bathy and abyssopelagic.
5. (through 10) Abundance of phyla, expressed as % of the considered domain.

In my opinion a PCA and a MDS are not useful for this kind of data. I'm trying to evaluate the relation between the abiotic variables (salinity, etc.) and the abundance of the phyla.

What type of analysis can be useful to see the relation between Phyla abundance and abiotic variables like salinity and depth (see dataset example at link)?

Answer 1

Your outcome variables, the relative abundance of phyla, all add up to 1. So your outcome is really a set of compositional data. One issue: although your data show 5 different phyla, you only have 4 linearly independent values among them for each sample. Another issue: your data only represent relative abundance, not overall abundance. Sometimes overall abundance also needs to be considered.

It's not surprising that this is giving you some trouble, as rigorous systematic methods for statistical analysis of compositional data are only a few decades old. (See the link above for a general introduction and further reading.) It is possible to do regression analysis on compositional data but some specialized approaches are needed. For your type of application, this recent freely-available paper would seem to be a good introduction. Don't think that you can do this easily in Excel.

One more thought: you might not have enough data to adequately assess all of these predictors. There are 120 combinations of the levels of predictors 1 through 4, so 200 samples represents less than 2 samples per possible combination. That might lead to overfitting, providing a model that fits your data sample well but might not generalize to other samples.