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I run a Box-Cox transformation for a linear model to find an appropriate transformation for a response variable, which is a number of insect per sq.meter. I need to transform the response variable because of a pattern in the residual plot obtained after running the linear regression using none-transformed response variable. I used a boxcox() function from the ‘MASS’ package in R. Box-Cox suggested the best lambda value of 0.055 for transformation, which is close to 0 and corresponds to natural log transformation (Osborne 2010).

My question is may I use log10 transformation instead of natural log transformation? log10 transformation is the most common transformation my field. Are there any references, to back up this decision?

Just to mention, I can’t use Poisson regression because I work with averaged values of insects per sq.m, it is complications of using different sampling equipment.

Thanks enter image description here

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Anna Belyaeva
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    The base of logarithms is immaterial except for convenience and makes no differences to effects on skewness, heteroscedasticity, nonlinearity or whatever else is targeted by a transformation. Some readerships might be puzzled by natural logarithms; others regard anything else as unnatural. – Nick Cox Sep 05 '16 at 20:52
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    The most striking feature in your plots is observation 7. Is there any scientific explanation for it? – mdewey Sep 05 '16 at 20:52
  • Dear mdewey, lake #7 had an enormous population of this organism. Each sediment sample taken in that lake had hundreds of midges. It is not an entrance, identification, or sampling error. That lake just had a huge population of them. I have 400 variables associated with that lake and I do not see any unique features about that lake or habitat. – Anna Belyaeva Sep 05 '16 at 22:21

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Yes, you can! All logarithms are proportional, so the results will be identical, the proportionality constant will just change the estimated coefficients. Too see this: $$ y = \log_e x ~~\text{then} \\ e^y = x ~~\text{and then} \\ \log_{10} x = \log_{10} (e^y) = y \cdot \log_{10} e \approx 0.434 \cdot y $$ so estimated coefficients will change only by that constant $0.434$, the fit of the model will be identical, and hypothesis tests and so on will give identical results.

Nick Cox
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kjetil b halvorsen
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