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I am using a linear-log model to test whether overseas development assistance and remittances positively affect FDI in cases of good governance and financial market development. Let's say I want to interact the log of net official development assistance received (ODA) with governance. Governance is estimated as a score from -2.5 to 2.5. So I cannot apply the log transformation to governance, but can I still interact the log of ODA with governance? My hypothesis is that ODA will positively affect FDI in cases of good governance.

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Your use of the term "linear log model" is a little confusing for me. I think you mean a linear (OLS) regression model in which some (or all) of the explanatory variables have been transformed by taking the log. I've never heard that term before & I don't think it's standard. You should know that there is a standard term called the "log linear model", which allows us to analyze multi-way contingency tables. You will have an easier time communicating w/ people if you keep these facts in mind. –  gung Mar 30 at 7:04
    
If you read gujrati, you will understand that there are different functional forms of regression, where the linear-log model is included. –  user3472563 Mar 30 at 7:07
    
Hmmm, I do see that, section 6.6 "SEMILOG MODELS: LOG-LIN AND LIN-LOG MODELS". It's been a long time since I looked at that, I suppose I'd forgotten. Nonetheless, I would avoid using those terms, they really aren't standard in statistics. In particular, people will confuse the log-lin model w/ the log linear model, which are not the same thing at all. I would say, 'a regression model w/ a log transformed predictor' or 'a regression model w/ a log transformed response variable'. –  gung Mar 30 at 7:13
    
thank you for the advice. I will change the wordings then. Thanks. –  user3472563 Mar 30 at 7:15
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1 Answer 1

Linear models (i.e., OLS regression) do not make assumptions about the distribution of explanatory / predictor variables, except that they are known constants. (To learn more about the assumptions of linear models, it may help you to read this thread: What is a complete list of the usual assumptions for linear regression?)

You are free to transform any, some, all, or none of your variables as you choose. Some reasons for choosing to do so are listed in this excellent answer by @whuber: In linear regression when is it appropriate to use the log of an independent variable instead of the actual values? The interpretation of log transformed variables is well explained in this thread: Interpretation of log transformed predictor.

Outside of these issues, the existence of an interaction, or the fact that the transformed predictor is included in an interaction, does not change anything.

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Thanks a lot for your help @gung –  user3472563 Mar 30 at 8:36
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