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I have to model 5 variables (in the same model to test for the most important factor) which include measures of distance (m) and percentages. At the beginning, I transformed the variable distance to log(x), as it seems to be the general recommendation for distance/area variables... Then I scaled all the 5 variables to z (as I understand it is correct when comparing multiple models or variables with different scales as in this case). However, I just want to confirm if it is ok to double transform in this way, or if I should just rely on z values from the raw data and do not transform distance measures previously. [just in case: my response variables is abundance of species, and the predictors are cover (categorical), percentage of forest, distance to roads, distance to towns, and ndvi-a vegetation index related to the reflectance of plants-; I´m using GLM for multivariate abundance data in mvabund package). Many thanks in advance.

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    $\begingroup$ A log transformation is important and may make or break an analysis. Working with z scores is at most a convenience linear transformation and just affects how coefficients are reported. A simple analogy is converting between temperature scales: some countries still use Fahrenheit but science uses Celsius or kelvin: if you change scales your results will change superficially but how good a model is will be unaffected. $\endgroup$ – Nick Cox Aug 6 '16 at 8:39
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I'm curious, what makes you think it is not valid? I see no problem with transforming variables if you can justify the reason for the transformation. Making n transformations to an independent variable is equivalent to making 1 if the function is.

For example, if $f(x)=\ln(x)$ and $g(y)=\frac{y-\mu_y}{\sigma_y}$ then $h(x)=g(f(x))=\frac{\ln(x)-\mu_{\ln(x)}}{\sigma_{\ln(x)}}$.

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  • $\begingroup$ If this is intended as an answer rather than a comment, would you mind expanding on it a little? $\endgroup$ – Glen_b Aug 6 '16 at 5:46
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    $\begingroup$ Honestly, I don´t know. I log transformed my variable first as it is commonly preferred to interpret measures of distances and areas as “order of magnitudes” as oppose to the actual value, but then I thought transforming that again to z would be a mistake. Thanks to the feedback here, I conclude it is not a problem, them. Thanks much $\endgroup$ – lep Aug 7 '16 at 22:24

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