Calculated Rao Q in hillR and FD packages are different about hillr HOT 3 CLOSED

The differences between results from FD and here is because of different formulas used in calculating RaoQ.

FD uses ade4::divc() to calculate Rao's Q, which is (here for source code lines 564-565):

     `div[i, ] <- (t(df[, i]) %*% (as.matrix(dis)^2) %*% df[, i])/2/(sum(df[, i])^2)`

See that instead of use formula $\sum \sum p_{i} d_{ij} p_{j}$, they used d_ij ^2 and then divided results with 2 and then (sum(df[, i])^2).

Instead, in my code, i just used the original formula $\sum \sum p_{i} d_{ij} p_{j}$, c.f. Chiu and Chao 2013 Plos One.

If you change the FD code, (lines 564-565 in the above url) to div[i, ] <- (t(df[, i]) %*% (as.matrix(dis)^1) %*% df[, i]), we get the same results.

Another possible result for potential differences between results from FD and here is the many many pre-calculation data manipulations.

Thanks for your comment.

from hillr.

I've checked both of codes, and I noticed it before, Chiu and Chao 2013 formula for Q is as the Botta-Dukát 2005 (FD refers to this article for Rao's Q formula).
I don't know why FD use ^2 and /2 in it's code.
Thanks.
p.s: It will be great if you implement hill phylogenetic diversity in your package.

from hillr.

I think the FD::divc() and ade4::divc() used d_ij^2 and then divided 2 and sum of d_ij^2 to try to standardize Rao's Q results, so they are less dependent with the number of species. I am not sure how effective is it. But, if one will use something like null models to account for species richness, then it will be better just use the original formula $\sum \sum p_{i} d_{ij} p_{j}$.

from hillr.