Is it necessary to perform a transformation on proportion data if it's reasonably well behaved?

Question

If you're modelling a proportion response against numerous predictors that are also proportions, is it necessary to transform the response if the standard OLS model is seemingly well behaved?

By well behaved I mean:

• None of the fitted values are outside the range [0,1] (In fact they are fairly accurate)
• Residuals look good

I believe arcsine transform is typically used in this scenario to make the data look normal, but what if this is not needed?

Also, say the data wasn't normal, would a transform still be necessary if one were modelling the proportions with the Random Forest technique?

Cheers

Answer 1

It depends. If your goal is prediction, then you may not need to do any gymnastics to get a more theoretically sound model if the one in hand does well. But of course you should be always be aware that a good-fitting model to present data may not perform well on new data. You can try to get a feel for that using cross validation, although you simply might not have important aspects of the distribution represented in your sample.

If you want to make inferences using some of the parameters in the model then that model should be motivated by the problem at hand.

Anyway, a first step is to just look at the response. Is it roughly bell-shaped? Did you try the arcsine transform? Does the transformed distribution look (much) different? If the distribution of the proportions is fairly tight and located somewhere in the middle the transformation might not do much. And then, of course, does the transformation make a difference in the regression?