Does logging gdp per capita improve my model (comparing non-nested models)?

[Paul Connor]

Hi all,
I'm trying to run multilevel models with individuals nested in countries. My question is about whether or not to log gdp per capita. I want to include it in the model as a between cluster variable, but i'm not entirely sure which model is better - the one with gdppc logged or just gdppc. So far I've really only learned how to compare nested models, and these models are not nested.

The log-likelihood of the gpdpc logged model is closer to zero, and the Wald statistic is higher, so i'm guessing this means that the logged model is doing better in this case. Is this a safe assumption?

Thanks,

Paul

[Carlo Lazzaro]

Paul:
welcome to the list.
Your question is difficult to reply (for me, at least) as you did not post what you typed and what Stata gave you back (please, see the FAQ on this an other topics).
That said, the convenience of logging variables such as gdp, income or the like in a regression setting, when they're dependent ones, rests on the possibility of expressing in percentage terms their change for one unit increase of each independent variable (when adjusted for the other predictors).
This procedure may sometimes reduce heteroskedasticity of the residual distribution (event though it can well produce the opposite effect).

[Nick Cox]

However complicated your model, it should be possible to plot observed versus fitted and residual vs fitted. Such plots can you give you signals on which functional form is better for your data.