# Different Transformation of the same IV [closed]

Suppose I've a panel data with 2 segments. And I want to run pooled OLS regression. I'm doing data transformation for each segment separately. Say for segment A, I'm doing log transformation and for segment B I'm doing square root transformation of the same variable. Is it possible?

• This would benefit from much more detail about what you did, as well as why. Commented Jul 16 at 10:16

## 2 Answers

Naturally it's possible. You did it.

Your question is presumably whether it's a good idea. Question in turn: Why did you choose different transformations in different models?

There are many myths about transformations, but the main reason for transformation should be that it helps with the functional form $$Y = Xb$$.

Otherwise the issue is as much substantive as statistical. There may be good substantive reasons for the functional form being different in different "segments", whatever they are, but otherwise choosing different models raises a need to explain to your readers why you did that. That applies to anyone, whether their readers are teachers grading an assignment, a committee reacting to a thesis draft, or reviewers looking at a submitted journal paper.

Detail: Many economists and some others mean instrumental variable by IV. That seems unlikely here, and if not then there are many better terms than the tired independent variable, such as predictor, explanatory variable, covariate, and many others.

I agree with everything Nick said here (except that I still use "independent variable"). I'd just add that, unless you have strong substantive reasons for your somewhat unusual choice, then there are very flexible ways to fit models that let the shape be almost anything. One is the whole panoply of splines. I usually use restricted cubic splines, from what I can see, these seem to be the default choice for quite a few experts, but I'm not a fanatic about it and there are many other forms. Another possibility (which I have only used once) is fractional polynomials).

• (+1) I don't think @NickCox objects to the use of "independent variable," as much as he objects to an unintroduced, possibly ambiguous abbreviation. Commented Jul 16 at 10:00
• Thanks for the agreement! Reasons for (anyone else) to avoid the terminology independent variable: (1) different meanings of dependence and independence abound in statistical science (2) many students (and others!) get the terms the wrong way round, remarkable though that may seem (3) more evocative alternatives abound. Commented Jul 16 at 10:00
• @FransRodenburg You are half-right. I don't like the term independent variable but manifestly I don't have, and absolutely I don't want, any power to forbid it. I just try to persuade people away from it. Commented Jul 16 at 10:03
• @NickCox Yeah, we've discussed this before. Probably no need to get into it again. Bu I also have problems with 'predictor" and "explanatory" and I like to save "covariate" for variables that I am not particularly interested in. Also, "instrumental variable" seems liess common in the fields I usually worked in. Commented Jul 16 at 10:03
• Indeed. That is why I added "(anyone else)" -- not that you're unreasonable, just unlikely to change. But it's factual that some people use IV as abbreviation for independent variable and some use it as abbreviation for instrumental variable. Any confusion is unlikely to last long if you're given sight of someone's results or software syntax, but clarity beats confusion, with nothing else said. (Further, DV means Deo volente, too, but that ambiguity doesn't bite in my experience.) Commented Jul 16 at 10:07