Log Transformation

[Tess Gecha]

Hello,

Should you ever log transform ordinal data? Or can you only log transform continuous variables?

Best,
Tess

[Mead Over]

No firm rule. It depends on your application and data. Is the ordinal variable a dependent variable or an independent variable? How many distinct levels does it have? Are there multiple ordinal variables in your model? Would treating the ordinal variable as if it were continuous be meaningful to your audience? Does the ordinal variable contain negative or zero values which will be transformed to missing values by the log transformation?

If your only purpose is to capture non-linearity in an independent variable, would your purpose be better served by expressing the ordinal variable as a -factor variable-? An examination of the coefficients of the factor variable in a regression model would either support or cast doubt on the assumption that the true functional form is logarithmic.

[Nick Cox]

I've never yet met an ordinal variable that benefitted from logarithmic transformation. Examples to the contrary would be interesting.

I'd also query #1 in that Poisson regression for counted responses is essentially based on the idea that relationships are exponential. The twist is that doesn't mean log transformation of the response or outcome, if only because that would often be problematic if zeros are present. Rather, the recipe is to use what in generalized linear model jargon is a logarithmic link function.

[John Mullahy]

In addition to #2 and #3, assuming you are considering the ordinal variable as your outcome (or LHS) variable, then it shouldn't matter whether you take a log or any positive monotonic transformation of it so long as you focus on parameters appropriate for ordinal measures, e.g. medians/quantiles but not means/variances/moments.

One classic reference is: https://www.jstor.org/stable/1671815