I am a longtime user of glm() and lmer() and for the most part I know what Im doing.
At the moment Im 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 Id *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 cant 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 Id 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]]
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