For an nxp matrix of species abundances, I have coordinates of the n sites. In order to use the species abundance data for spatial modelling or redundancy analysis, I note that in the literature, as a preprocessing step, it is recommended that the species data be Hellinger-transformed, and then detrended by regressing the species abundance data on the geographic coordinates, to remove possible linear gradient effect.
I can understand that the residuals from the linear regression no longer contain the spatial information, but this would mean that the resulting pre-processed species abundance data matrix contains some negative values (a (pre-processed)species abundance matrix with negative values just feels weird). Would this be a potential source of strange results later? I would be interested to hear about the experience of researchers who have come across this situation. Thanks.
Hellinger involves dividing each value in a data matrix by its row sum, and taking the square root of the quotient, so it won't produce negative numbers. And detrending involves absolute values, so I'm not sure how negative values arise?
Hi Andrew,
The detrending occurs after regressing the Hellinger-transformed data on the xy coordinates and using the resulting residuals, which can be negative.
Negative residuals are not a problem – they just mean the actual value was LESS than the predicted value
Let's consider a simple situation where only x coordinate applies (transect). When the intercept of the regression line is negative, the expected species abundance (Hellinger transformed) is negative below some threshold value of x, and if I have 0 abundance observed at the origin, I would get a positive residual (abundance higher than expected), but what is expected is non-sense (negative abundance). I wonder how to make sense of the residual matrix then?
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