If you need to log-transform both the outcome and predictor variables, you certainly have a nonlinear relationship between the two, most probably a power relationship, i.e.:

Y=aX^b

Where "a" is a coefficient and "b" the exponent of the predictor X. When you log transform both sides of the equation, you obtain log(Y) = log(a) + b*log(X), a linear equation.

The best way to handle this is to analyze the data with a nonlinear mixed model, where the above power equation is specified as the structural component of the model. This analysis can be done with a specific software for nonlinear mixed models such as NONMEM, or with advanced statistical software such as SAS, S-plus, R, etc.

As for references, you may find lots of them in the field of interspecies allometric scaling. I suggest you the following that comes from my field of work:

Martín-Jiménez T, Riviere JE. Mixed-effects modeling of the interspecies

pharmacokinetic scaling of oxytetracycline. J Pharm Sci. 2002 Feb;91(2):331-41.

PubMed PMID: 11835193.

Good luck with your analysis!

Thank you for your help,Jerome del Castillo !

I will try it out that.

I want to directly interpret the log transformed mixed model , like % change in X effect the % change in Y.

I have not get any reference for that!

Is your data in percent values, or you are going to describe that in the results section of a manuscript? I would like to warn you about the problems of analyzing percent data. They often end up with wrong interpretations because the percent transformation can either magnify a non-significant difference between groups or shrink a significant difference. Also, if your data is bounded between 0 and 100%, the closer your means get to the boundaries, the more they violate the assumptions of the general linear model. See the following article:

Kronmal, R.A. (1993) Spurious Correlation and the Fallacy of the Ratio Standard Revisited. Journal of the Royal Statistical Society Series a-Statistics in Society, 156, 379-392.

Hi Jerome R E del Castillo!

Thank you for your valuable comments and help.

My data actually child anthropometric measurements over 2 years ,which is not linear so that I transformed data into log values .ie) log(y)=a+log(x).so that I want to interpret into percent change.

Is this correct?

http://en.wikipedia.org/wiki/Data_transformation_(statistics)

Thanks again!

Hi Karthikeyan Ramanujam! I'll write you a personal message so I can ask you some specific questions about your dataset and provide you the best advice I can.