Can I take logarithms of magnitudes (which are already log) I'm investigating the relationship between the magnitude of quasars in various wavelengths, and their redshift $z$. I've found that if I take the $log$-$mod$-transform ($L_{mag}$) of the magnitudes, where

$L(y) = sgn(y) * log(|y| + 1)$

which I got from here and here, I can get a slightly tighter fit for my data, which is the aim of the study. Here's a plot for the W1 magnitude and $L(W1)$ as above, both against $log(z)$:



showing the regression coefficient for each.

My question, before I take this to my supervisor, is: is there any reason why I shouldn't be taking the $log$ of an already $log$ quantity?
You can, the question is whether you should.

Is there a theoretical reason why you think that magnitude should vary exponentially with redshift? If not then you may be falling into a fallacy.

You see with a polynomial with sufficiently many terms, I can get a curve that fits your data perfectly, r=1, Does this my polynomial is a better model? Probably not.  Just throwing functions at your data and choosing the one that gives the biggest r isn't mathematical modelling of data.

I would question why you are using magnitude at all? You seem to be finding that "close objects appear brighter" which isn't a new discovery.