Is Hellinger transformation suitable for repeated (in time) site-species abundance data?

Question

I have fish survey data from four different years and several locations, where I would like to study the difference in abundance and biomass between sites and check whether time dependence influences the significance in differences found between the sites. Because my data contains a lot of zeros and low values I believe using Hellinger transformation will be appropriate. However I am not sure if I can use this transformation on repeated site-species data. If it is possible, can anybody send me a link or info on how I can/should apply this transformation? I have not been able to find a study where they applied Hellinger transformation on similar data.

Answer 1

Yes, it's fine to do this. You apply it in the same way as you would for non-repeated observations.

Say you have a matrix $\mathbf{Y}$ of biomass values with dimensions $i,j$ where $j$ indexes the species and $i$ indexes the samples, the Hellinger transformation is

$$y^{\prime}_{ij} = \sqrt{\frac{y_{ij}}{y_{i+}}}$$

where $y^{\prime}_{ij}$ is the transformed biomass for species $j$ in sample $i$, $y_{ij}$ is the observed biomass, and $y_{i+}$ is the row sum over the $j$ species for the $i$th sample.

There is nothing in this transformation that relates to time or particular observations. There is nothing here that is going to get messed up by applying this to repeated observations. Just arrange each observation as a row in your response matrix $\mathbf{Y}$, arrange the species in the columns, and then have the meta data (site, time, etc) in a separate matrix in the same row order as $\mathbf{Y}$, to keep track of which samples come from which sites, times, etc.