For linear regressions between linear measurements and body mass, which transformation is better to use? base e logarithm (LN)? or base 10 logaritm (LOG10).
Apparently they do not make such a for data transformation, but there might be a difference of which I am not aware, regarding body mass estimates. Any suggested references on this subject would be greatly appreciated.
they differ by a constant only, use what you like:
(log(x) to base 'e')/(log(10) to base 'e' =log(x) to base '10'
1. log(100) to base 'e'=4.60517186
2. log(100) to base '10'=2
3. log(10) to base 'e' = 2.302585093
thus (1)/(3) = (2)
You might have a look at the huge work of S. Legendre (1989) which allowed to apply the cenogramm method to fossil communities, based on the very strong correlation between the tooth area and the body-weight in recent mammals. Serge Legendre evaluated as follow the body weight from the first lower molar, using for calculation the parameters of the allometry between these two factors:
Ln(weight) = Ln(b) + [a * Ln(Y)]
with a=coefficient of allometry, b=constant and Y=surface of the first lower molar (m1)
Legendre, S (1989). Les communautés de mammifères du Paléogène (Eocène supérieur et Oligocène) d’Europe occidentale: structures, milieux et évolution. Münchner geowissenschaftliche Abhandlungen (A). Geologie und Palaeontologie, 16, 1-110.
they differ by a constant only, use what you like:
(log(x) to base 'e')/(log(10) to base 'e' =log(x) to base '10'
1. log(100) to base 'e'=4.60517186
2. log(100) to base '10'=2
3. log(10) to base 'e' = 2.302585093
thus (1)/(3) = (2)
Transforming the variables, both the response variable and the input variables, is most often dictated by choice for a simplistic, easily interpretable model and at the same time satisfying the statistical assumptions associated with significance testing of regression models, therefore, of the two alternatives you proposed i suggest you go with that form for which the residual diagonistic plots appear better satisfying the criteria.
ps:
I should have said that, if using base '10' then the CONSTANT " log(10) to base 'e' = 2.302585093 "
will cause PLOT to shift (offset) up the y-axis...remember when interpreting your data...
NB: we use base 'e' because growth curves tend to be similar to the Mitscherlich (simple exponential) function.
I agree with Debopam Ghosh, it is an attempt to meet the assumptions of the statistical analysis to be employed, especially those of normality and homoscedasticity. Do a data exploration and see which transformation that best suits your data, especially a biological data such as yours. See the attached for detail. Do not forget to back-transform before submission.
For engineering applications and calculations LN is preferred. For graphical representation and to have a sense of impact of data connected with powers of 10, LOG10 can be adopted.
Jorge -
What about a quadratic "linear" regression? Jim Frost has a nice blog, "Statistics by Jim," where he explains this. Also, heteroscedasticity is a natural phenomenon, to be expected. Logs will sometimes do, but transformations can cause problems in interpretation, are messy in my opinion, and you may still have substantial heteroscedasticity.
There is an example of handling heteroscedasticity in the following, for a quadratic linear regression borrowed with permission from the blog above:
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity
To do this, if your software will do quadratic or even higher polynomial regression, then you can collect the y-values, and corresponding homoscedastic predicted-y-values, and the following spreadsheet will help you find a reasonable coefficient of heteroscedasticity to use to then rerun that software with regression weights, assuming such software will let you input regression weights:
https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx
Best wishes - Jim Knaub
Dear Moreno-Bernal, I dare to say...neither one.
Please refer to:
1) Araujo, R.P., Vieira, R.A.M., Rocha, N.S., Abreu, M.L.C., Glória, L.S., Rohem Júnior, N.M., Fernandes, A.M., 2015. Long-term growth of body, body parts and composition of gain of dairy goat wethers. Journal of Agricultural Science 153, 1321-1340.
2) Vieira, R.A.M., Rohem Júnior, N.M., Gomes, R.S., Oliveira, T.S., Bendia, L.C.R., Azevedo, F.H.V., Barbosa, D.L., Glória, L.S., Rodrigues, M.T., 2018. The ontogenetic allometry of body morphology and chemical composition in dairy goat wethers. Animal 12, 538-553.
If you have any questions about SAS program sentences or R codes, please let me know.
Yours sincerely,
RAM Vieira
RAM Vieira -
Are you using polynomial linear regression?
Are you accounting for heteroscedasticity?
If not, might you summarize your approach?
It appears that Jorge is trying to handle a curved relationship, and heteroscedasticity should generally be there as well.
Anyone else have a comment?
Cheers - Jim
PS - I agree with Debopam in principle, although in this case Mewa showed that it won't matter. But generally, a "graphical residual analysis" will be very good for exploring model fit, and a "cross-validation" might be used to study whether you have overfit to your particular sample.
Please refer to those two papers I've mentioned. There are problems related to the probability distribution of the variable, correlation if measures are taken on the same subject and heterogeneity, because variability of most variables is a function of scale.
I am not using polynomials. And I strongly recommend the Information-Theoretic approach to evaluate quality of fit. Residuals will depend on the probability density function you choose. Concordance correlation coeficient is another valuable measure of model fitness.
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