Hello ecolog, Thanks to all of you who responded to my question about data transformations suitable for my power analysis of percent cover data (original post is repeated at the bottom of this summary).
A number of people suggested the standard transformation for percent cover data, the arcsine square root transform. While this transformation would have bounded the data between zero and one, it has the undesirable side effect of being non-monotonic, which would have been an issue with my simulated data. Several people pointed me towards a recent paper, Warton and Hui 2011 (Ecology 92:3-10). These authors propose a modification to the logit transformation, specifically adding a small value to both the numerator and denominator of the logit function. This is the approach that I am now pursuing with my analysis. There is clearly a lot of debate back and forth about the merits of transforming data, and the difficulty of interpreting the output when transformations are used, and I appreciate the recommendations I have received about using data transformation sparingly. I tend to agree with these comments, but in this case I feel that having a simulation with realistic data and meaningful predictions outweighs the difficulties of back-transforming and interpreting the output. Thanks again for the helpful feedback to my query! Original post: 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 dont 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 Ive 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? Brian Mitchell NPS Northeast Temperate Network Program Manager Adjunct Assistant Professor, University of Vermont [email protected]
