Hi Brian, I've been encountering this percent cover issue for a while. Unfortunately my data was all based on Braun-Blanquet estimates so analysis has been tricky. I converted to midpoint percent estimates (not strictly legitimate but served the purpose) and then had the same problem you did.
I've been using the logit transform, log(y/1-y). And yes, you do have to add a small error term. I found the following caused the fewest problems (although it looks quite messy): log[((Y*0.998)+0.001)/(1 -((Y*0.998)+0.001))] I seem to recall that just adding 0.001 (or some other such small number) gave greatly inflated values for points close to 1 (I could be wrong, sorry, my 1 year old is clinging onto my leg while I write this - I may have a few too many brackets there as well!!). There is a great reference for this but I don't have all the details in front of me (and now have banana all down my good pants!!): Type into google: "The arcsine is asinine" by Warton et al It gives a great justification for using the logit transform and also explains why a GLM (logit link) isn't so appropriate for % cover data (it's quite tempting to use). Hope this helps, Liz On Wed, Nov 30, 2011 at 6:33 AM, Brian Mitchell <brian.mitch...@uvm.edu>wrote: > Hello ecolog, > > I am working on a power analysis simulation for long-term forest monitoring > data, with the goal of documenting our power to detect trends over time. > The simulation is based on a repeated measures hierarchical model, where > future data is simulated based on the initial data set and a bootstrap of > pilot data differences between observation periods, multiplied by a range > of > effect sizes (50% decline to 50% increase). > > My question is about the appropriate transformation to use for percent > cover > data in this simulation. I don’t want to use raw percentages because the > simulation will easily result in proportions less than zero or greater than > one. Similarly, a log transform can easily result in back-transformed > proportions greater than one. Most other transforms I’ve looked at would > not prevent back-transformed data from exceeding one or the other > boundaries. The exception is the logistic transform, which would indeed > force all simulated data to be between zero and one when back-transformed. > However, the logistic transform gives values of negative infinity for a > percent cover of zero, and positive infinity for a percent cover of one. I > was thinking that adding a tiny number to zeros and subtracting a tiny > number from ones (e.g., 0.00001) would solve the problem (roughly > equivalent > to a log of x+1 transform), but I have been unable to find reference to > anyone using this approach for percent cover data. Does anyone have any > thoughts about the validity of my proposed approach or of another approach > that would help solve my problem? > > Thanks! > > Brian Mitchell > NPS Northeast Temperate Network Program Manager > Adjunct Assistant Professor, University of Vermont > brian_mitch...@nps.gov > -- Liz Pryde PhD Candidate (off-campus) School of Earth and Environmental Sciences James Cook University Thornbury, Melbourne
