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OK, I have been reading around on how to interpret transformed models, ... including this thread:

Analysing log and square-root transformed variables

I am interested in the OP's (of the link above) question in terms of using multiple transformations in the same model. Lets say I have proportion data on 3 land cover categories used as IVs in OLS regressions. The issue is that 2 of the 3 variables are skewed to some degree.

One land cover variable is positively skewed; this is alleviated to some degree with the arcsin sqrt transformation, and the other is negatively skewed and this is alleviated by log10 transformation. Could someone explain to me 1) if this is OK, and 2) how to interpret the results as is done here:

Interpretation of log transformed predictor

I would like to be able to compare the relative influence of these predictors.

An alternative would be to retain the log transform on one land cover variable, and not transform the other two. If this is done, how could I compare the relative effect of the land cover variables on a particular Y?

Unfortunately, it seems what is good for the goose in this instance is not good for the gander.

Thank you for any help. Patrick

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    $\begingroup$ You might want to add why you want to transform these explanatory variables. They do not need to be normally distributed for OLS. $\endgroup$ – Dimitriy V. Masterov May 8 '13 at 21:38
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Unless there's a substantive theoretical issue that is specific to your field, I think it will be hard to justify transforming similar or identical types variables in different ways, for what's-good-for-the-goose-should-be-good-for-the-gander reasons.

Take a look at the Transformations for proportions and percents section in Nick Cox's transformation intro. Perhaps there will be something there that will work for all three proportions, and then we can work on the coefficient interpretations.

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  • $\begingroup$ I have restated the problem above; I hope that clarifies the issue. $\endgroup$ – Patrick May 8 '13 at 22:40
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    $\begingroup$ In response to your clarification, let me correct this common misconception. OLS does not require your right-hand-side, explanatory variables to be normally distributed. Transformations of RHS variables may be helpful for theoretical reasons or analytical convenience, but least squares will work just fine without them. $\endgroup$ – Dimitriy V. Masterov May 9 '13 at 0:11

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