Order of Adonis test formula

[saatkinson (Samantha)]

Hello,

I've read in many other posts (ex: this and this) that the order of the variables matters when inputting the formula for the Adonis test. I have a beast of a formula (9 variables) and I'm not sure of best practices on how to order the variables.

From the first linked post, I understand that whatever variance isn't explained in variable 1 is passed down to the next term and so forth. Does that mean I should stack my variables to have the ones responsible for the most variance at the beginning?

For example, one of my human microbiome study variables is "relatedness," i.e. whether patients are first degree relations (there are 137 families total). It's well established that families/cohabitants will have more similar microbiomes, so should I list that first/early in my formula?

I have tested this theory a little and (with my data at least) if I run the formula with relatedness toward the end most everything before it is statistically significant, but if I run it was the first term nothing is statistically significant besides relatedness. Relatedness is basically stead with its R^2 value, 67% and 71% respectively.

I'm trying to determine the most unbiased way to run the test. Any and all thoughts/feedback would be greatly appreciated!

Thanks,
Samantha

[colinbrislawn (Colin J Brislawn)]

Hello Samantha,

It's great to see another one of your questions on the forums!

While this is a stats question, it's also related to scientific modeling.

@saatkinson

I'm trying to determine the most unbiased way to run the test. Any and all thoughts/feedback would be greatly appreciated!

Because your choice of order does matter, the choice of variable order changes what is being tested. How to ask this question reflects a viewpoint about these variables which will be (and should be!) biased based on a model of the world.

@saatkinson

if I run the formula with relatedness toward the end most everything before it is statistically significant, but if I run it was the first term nothing is statistically significant besides relatedness.

The formulas represent different models and measure different things.

I would write:
The following variables explained these effects of unifrac-distance between samples: age 7%, diet 9%, NSAID 2%, steroids 3%, etc. relatedness 67%
When first testing for relatedness, we observe no other significant factors, showing that this is the most important blocking variable.

I hope this is helpful! Let us know if you have more questions!