I am a longtime user of glm() and lmer() 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>

	[[alternative HTML version deleted]]

