Hi,
I am seeking your kind advice on the possible statistical distribution of the ratio (or log-transformed ratio)between two dissimilarity index.
I have N sites, and for each pairwise sites (site i and site j), I calculated their bray-curtis dissimilarity in two different ways. way 1: using all the species in each site. way 2: only using part of the interested species in each site. Now I want to compare the difference between the bray-curtis distances using the two different ways, and then check how the difference is regulated by environmental variables. So, I will conduct a GLM or GAM, and the response will be the ratio (or the log-transformed ratio) between the two types of bray-curtis dissimilarity.
Traditonally, as the bray-curtis distance is within the range [0,1] and can be considered as a kind of ratio, GLM will use bionomial distribution as the distribution of the bray-curtis distance. Now my question, however, is the distrition of the ratio (log-ratio) of two variables of this type.
Your suggestions will be much appreciated!
Why taking the log-ratio? Are the variables qualitative or quantitative? Qiang Yang please i need clarification, Thanks.
Jamilu Yunusa Falgore
Hi Jamilu,
When taking the log-ratio, the log(A/B) can be rewritten as log(A)-log(B). I was considering if the distribution of log(distance) can be easier to calculated.
When you say "GLM will use binomial distribution as the distribution of the bray-curtis distance" ... is this the conditional distribution of the "number in common" given the total across the two sites? (Which might be reasonable, otherwise an unconditional beta distribution on 0,1 might be useful).
In your case the change between the two variants of the bray-curtis distance is due to the absence or presence in the counts of the "non-interesting" species, so you could just represent the change using the bray-curtis distance for these "non-interesting" species (rather than using the difference or ratio.
Many thanks David. We indeed calculated the distance as the "number in common" given the total across the two sites. The problem for these 'non-interesting' species in our case is that, we have different sets of 'non-interesting species' for each pair of sites for which the distance is estimated.
Does it matter if "we have different sets of 'non-interesting species' for each pair of sites "? The same thing would apply if you just took the ratio as you originally indicated (since one of the measures is affected by the non-interesting species). If you are just trying to see how much of the "distance measure" is affected by non-interesting species, then this might be accomplished by looking at the distance measure for the non-interesting species.
It seems that your basic random variables are the "counts-in-common" ... these counts might be considered statistically independent for the "interesting" and "non-interesting" species, If you write whatever statistic you want to look at in terms of these random variables you can could evaluate the distribution exactly for given assumed parameters. If you just used the difference between two scaled counts, you can readily get expressions for the mean and variance (and higher moments).
- Badges
- Science topic