I'm trying to create a mixed model and I've both scaled and logged (log10) some of the explanatory variables. Residuals of the model are looking good. I was wondering whether there are any issues associated to using both scale and log on the same variables. The reason I'm doing both is that the effect from the covariates seems to be stronger when they are both scaled and logged.

Everything is being done in R with the base and glmer packages.

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  • $\begingroup$ The effect is stronger according to what measure? How many transformations did you try? $\endgroup$ – Frans Rodenburg Oct 24 '18 at 11:03
  • $\begingroup$ Essentially the z scores of the main treatment I have are significant if I scale, whilst they aren't if I don't. I initially logged data as it was both large and small values, however, perhaps it isn't needed. $\endgroup$ – Dasr Oct 24 '18 at 11:52

The effects can add up.

  • Using the logarithm of one or both $x$ and $y$.

    Here the functional relationship is different.

    The use of this makes sense when the actual relationship is logarithmic/exponential/power-law (it would not be good to ad-hoc start trying out all kinds of relationships just until you get some, more significant, stronger effects).

  • Scaling (where the function in R is also translation/centering and not just scaling) the variables can change the confidence intervals for estimates of coefficients (and also the significance of a t-test). The effect is due to the shift/translation/centering (not due to the scaling which has no effect on significance). An example is shown here (https://stats.stackexchange.com/a/364723/164061).

    Here the parameterization is different (the functional relationship is not changed).

    This translation has only effect on the coefficient estimates, and not on the ANOVA or other model comparisons. The residuals are unchanged and only the model has a different parameterization, but not different relationship.

    Use this scaling (different parametrization) when it makes more sense for representing the parameters/coefficients (e.g. the interpretation might be better/easier in some particular representation).

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