# Thread: Testing a log transformed reg model with the non-log transformed

1. ## Testing a log transformed reg model with the non-log transformed

Hello, I was wondering how one test two regression models against each other. One being the log transformed of the other like this:

y = var1 + var2 + var3...
log(y) = var1 + var2 + var3...

Are model (2) nested in model 1? And how does one best compare these two (a test), for which is the best model in total? If possible

2. ## Re: Testing a log transformed reg model with the non-log transformed

The problem concerns functional form. Models are not nested (rules out LR testing). Simple approach is to compare using information criteria. Another approach would be regression specification error test (RESET). However RESET only tests whether there is a problem of functional form in general in the model without the logged dependent variable. Not whether the problem is specifically related to the dependent variable not being cast in logarithmic form.

3. ## Re: Testing a log transformed reg model with the non-log transformed

What about Vuong test, though I cant remember what the test is for

4. ## Re: Testing a log transformed reg model with the non-log transformed

Thank you both for answers! I am not really sure what the result from the RESET test mean, but I guess if we find a reasonable p-value for one of them, we can keep this over the other.

5. ## Re: Testing a log transformed reg model with the non-log transformed

I don't think you should test these two models against each other, even if such a test were available. Certainly not a test based on R^2.

You should take the log of the DV if it makes substantive sense to do so; and not take the log if it doesn't make sense.

First define the problem, then find a solution. If you are even considering taking the log, the variable is probably skewed. If you decide that it doesn't make sense to take the log, you can use quantile regression. If you are using SAS, you can do this with PROC QUANTREG and methods are available in R and (I am sure) other packages as well. Quantile reg does not mind skewed variables - it's well suited to them.

Does taking the log make sense? One common case where it does is when the DV is monetary - salary or the cost of something - because we usually think of money in multiplicative terms, not additive ones. That is, if you are shopping for a house and the cost is around \$1,000,000 and they offer to take off \$10,000 - that's pretty small. But if the cost is around \$100,000 and they offer \$10,000 off then that is a lot.

I would transform monetary values with logs even if the result was more skewed than the original

6. ## Re: Testing a log transformed reg model with the non-log transformed

Originally Posted by PeterFlom
Does taking the log make sense? One common case where it does is when the DV is monetary - salary or the cost of something - because we usually think of money in multiplicative terms, not additive ones. That is, if you are shopping for a house and the cost is around \$1,000,000 and they offer to take off \$10,000 - that's pretty small. But if the cost is around \$100,000 and they offer \$10,000 off then that is a lot.
Just out of curiosity: Assuming we are modelling the price of a house and we are using a logged model such that dependent variable is log(price) and we also want to check for the added value of the house having an extra bathroom. One obvious strategy would be to include a dummy as independent variable indicating whether the house has an extra bathroom. But now the assumed constant beta-coefficient measures the percentage value added of having an extra bathroom. It does however seem - to me - highly unlikely that the effect in this case should be multiplicative. But then again one might imagine more expensive houses to have equally more expensive bathrooms. So perhaps both make sense and the choice of model is empirical?

7. ## Re: Testing a log transformed reg model with the non-log transformed

I don't know for sure, but I would guess adding a bathroom does have a multiplicative effect. One could check this with data, if one had enough.

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