Can we perform mean centering after log transformation

[Iqbal Chowdhury]

Hello everyone,

For my PhD papers, I am running a model with the interaction term between GDP per capita and immigration status (native born=1 reecent immigrant=2, and long resiging immigrant=3). The dependent variable is dummy of anxiety disorder (yes=0 and no=1). In this case, I have first mean centered the original GDP per capita variable and placed it in the model. However, the cosntant and 95% CI for immigrant category appeared very big (constant 709 and upper limit of CI is with 6 digits). Then, I log transferred the GDP per capita and placed it in the model. The same results appeared. Finally, I mean centered the log transferred GDP per capita and palced it in the model. The model appeared to be fine.

So, I am looking for any supporting documents concerning whether I can mean center a long transferred variable. However, I am not finding out any document.

I will appreciate if you kindly help me with this respect.

Your suggestion will be very helpful for my project.

Thank you in advance,

Iqbal Chowdhury

[Clyde Schechter]

You can mean-center any continuous variable for which a mean is meaningful. This is often helpful for simplifying interaction models, and especially for model with quadratic and higher-power terms. And sometimes it also stabilizes the calculations of the regression.

You cannot, however, log-transform a mean-centered variable because some appreciable fraction of the mean-centered values will be 0 or negative, and so have no logarithm.

[Iqbal Chowdhury]

Clyde Schechter
Thank you so much, sir. Would it be possible for you to share some documents supporting this so that I can share with my committee if needed?

Thank you once again. It’s a great help for me.

Iqbal

[Iqbal Chowdhury]

Clyde Schechter, also can you please help me with the issue. Can I first log transform and then mean center? I am sorry for disturbing you with multiple questions.

Thank you a lot.

[Clyde Schechter]

I don't think there is anything out there about centering vis-a-vis log transformation per se. The fact that you can't log-transform a centered variable because it will have zero and negative values is just high school algebra--I doubt anybody is going to publish a paper about that. There is some literature about general rules for when centering is helpful and when it is not. For example, the PDF downloadable from https://www.google.com/url?sa=t&rct=...U&opi=89978449.

[Bruce Weaver]

Iqbal Chowdhury, I believe the following demo answers some of your questions.

clear
sysuse auto
* Mean-center weight
quietly summarize weight
generate mcwt = weight - r(mean)
* Log-transform weight
generate logwt = ln(weight)
* Mean-center logwt
quietly summarize logwt
generate mclogwt = logwt - r(mean)
* Try to log-transform mcwt
generate logmcwt = ln(mcwt)
summarize weight mcwt-logmcwt

Output:

. summarize weight mcwt-logmcwt

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
      weight |         74    3019.459    777.1936       1760       4840
        mcwt |         74   -.0000111    777.1936  -1259.459   1820.541
       logwt |         74    7.978751    .2663436   7.473069    8.48467
     mclogwt |         74   -1.44e-09    .2663436  -.5056819   .5059186
     logmcwt |         39    6.233925    .6843437   5.014233   7.506889

N=39 for logmcwt because ln(mcwt) is missing when mcwt <= 0.

Re the other issue, if you really are concerned that committee members may give you grief about centering variables, it might be wise to cite resources that they will trust--i.e., textbooks or articles that are well-known in your field. What is your field of study? Someone may be able to point to such resources.

[Iqbal Chowdhury]

Clyde Schechter Bruce Weaver, thank you so much. Bruce, your example support that I can first log transfer and then mean center of a conitnuous variable.

I am in the field of Sociology and my project is dealing with the regional heterogeneity of mental health of immigrants. If you or any of you can provide me with a few suporting documents, that will be of great help.

Thank you once again,

Iqbal

[Bruce Weaver]

Your committee members may be familiar with the work of John Fox, who was a sociology professor at McMaster University. (His university site is no longer being actively maintained, which makes me think he may have retired.)

Paul Allison is another name that comes to mind. Try searching is statistical methods website.

Good luck with your work.

[Leonardo Guizzetti]

You may also consider the use of splines to model the effects of either the raw or log-transformed variable.

Do keep in mind that, as with any transformation, the interpretation of coefficients from the model will need to be carefully thought about. For example, in a normally distributed verified, centering the mean of the logged values means the coefficient refers to effects differing from the geometric mean.

[Iqbal Chowdhury]

Bruce Weaver and Leonardo Guizzetti thank you so much. Leorando, my question was whether I can first log transfer a variable (GDP per capita) and than mean center on it. Is there any technical problem of doing that? Is it statistically ok?

I think from the reaponse of Clyde Schechter and Bruce Weaver, I got the answer that I can first log transfer and than mean center on a variable before putting it in the equation. However, I cannot first mean center and then log transfer as there is no log for negative value.

Do you have any other comments? If you have please share with me.

Thank you all for your insightfull comments,

Iqbal

[Leonardo Guizzetti]

Yes I wasn’t disputing their answers, just giving additional food for thought.

[Clyde Schechter]

I think from the reaponse of Clyde Schechter and Bruce Weaver, I got the answer that I can first log transfer and than mean center on a variable before putting it in the equation. However, I cannot first mean center and then log transfer as there is no log for negative value.

That is correct.

[Iqbal Chowdhury]

Thank you so much, Clyde Schechter Bruce Weaver, and Leonardo Guizzetti for your great support. I will really appreciate if you kinsly share wiht me some documents.

Thank you once again,

Iqbal