[R-sig-ME] error distribution or transformation for Acid-neutralizing-capacity (ANC)

ONKELINX, Thierry Thierry.ONKELINX at inbo.be
Wed Apr 23 09:44:36 CEST 2014

A more radical approach is to alter the definition of ANC: take the ratio of the sum of cations and the sum of the anions rather than their difference. Then you can apply the log transformation without problems (assuming neither the cations or anions sum to zero).

Best regards,


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
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-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces op r-project.org [mailto:r-sig-mixed-models-bounces op r-project.org] Namens Ewart Thomas
Verzonden: dinsdag 22 april 2014 19:22
Aan: Brooks Miner
CC: r-sig-mixed-models op r-project.org
Onderwerp: Re: [R-sig-ME] error distribution or transformation for Acid-neutralizing-capacity (ANC)

brooks, try y = log(ANC + 17).  is the distrn approx normal.  i wd justify the offset of 17 as necessitated by the data, etc.  and it shdn't change your interpretation of originally negative values (now y < 17).

On Apr 22, 2014, at 8:37 AM, Brooks Miner wrote:

> I am a longtime user of nlme and then lme4 packages, and for the most part I know what I‚m doing.
> At the moment I‚m grappling with a particularly difficult response
> variable that I would like to analyze in a mixed-effects model: Acid
> neutralizing-capacity
> (ANC)<https://en.wikipedia.org/wiki/Acid_neutralizing_capacity> (
> http://en.wikipedia.org/wiki/Acid_neutralizing_capacity ). Although a
> very important measurement for lakes and streams, especially those
> recovering from acidification, ANC has difficult properties as a
> response variable: for example, in my current dataset the values range
> from -16 to ca. 400, and they are not normally distributed by any
> stretch of the imagination (see this figure:
> http://www.eeb.cornell.edu/miner/images/ANC_histogram.png )
> There are negative values that are really important because they indicate water bodies in especially bad shape (called „Acute Concern‰ by the National Acid Precipitation Assessment Program).
> I have time-series data for ANC from 1988 to the present for 60 sampling sites, and I‚d *really* like to use a mixed-effects model, with a random effect of „Site,‰ to model how ANC values have been changing over time, overall across the 60 sites. A random effect for „Site‰ is an ideal way to deal with the temporal pseudoreplication inherent in the time-series data.
> My challenge: how to deal with my non-normal ANC response variable using lmer() or glmer()? Of course when I run it with a Gaussian error distribution, the Q-Q plot of residuals looks terrible. Because of the negative values, I can‚t log- or sqrt-transform, use Box-Cox, or use family=„Gamma‰. All of the existing literature analyzing ANC time series uses non-parametric methods (such as a Mann-Kendall test), but I‚d really like to move beyond that in order to take advantage of a (G)LMM in order to draw general conclusions across all 60 sampling sites.
> Any suggestions for how to deal with this frustratingly unique ANC response variable?
> Many thanks ~
> - Brooks
> ***************
> Brooks Miner
> Postdoctoral Fellow
> Department of Ecology & Evolutionary Biology Cornell University
> www.eeb.cornell.edu/miner<http://www.eeb.cornell.edu/miner>
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