[Q]: Why are data recentered in the robust CLR transformation?

[Preve92]

Related to issue #570

I am trying to understand the implementation of the robust CLR transformation (

vegan/R/decostand.R

Line 197 in 802c826

.calc_rclr <-

). Specifically, the act of recentering after matrix completion.

This confusion arises from the differences I observe in taxa evenness. For example, in the two attached figures, the sample evenness (or lack thereof) is lost with the rCLR transformation with zero-imputation, but not in the other transformations (sample.png). Similarly, the dominant taxa across all samples now appears centered to zero, which, if I understand correctly, indicate average abundance (methanothrix.png).

Could you please help me understand why the centering is done and why the zero-imputed data are so different from the other transformations?

Thank you in advance for your time, and thank you for the excellent package!

[jarioksa]

The current implementation of vegan::optspace does indeed two things that may reduce the range of data values:

1. It centres columns which is not a standard part of rclr. @antagomir may be able to comment on this. (Centring rows is an integral part of the method, and re-centring adjusts this by using imputed values instead of original values with ignored NA values.)
2. It replaces observed values with a low-rank singular value decomposition made to fit to original observed values. It does not only impute NA values (original zeros), but replaces all values. The optimality criterion is a close fit of imputed values to original non-zero observations, but this cannot be very accurately achieved with low-rank SVD and this typically reduces the range of values.