I have a question about the correct distribution to use for creating a model with my data. I conducted a forest inventory with 50 plots, each plot measures 20m × 50m. For each plot, I estimated the percentage of tree canopy that shades the ground. Each plot has one value, in percent, for canopy cover. Percentages range from 0 to 0.95. I am making a model of percent tree canopy cover (Y variable), with a matrix of independent X variables based on satellite imagery and environmental data.
I am not sure if I should use a binomial distribution, since a binomial random variable is the sum of n independent trials (i.e., Bernoulli random variables). The percentage values are not the sum of trials; they are the actual percentages. Should I use gamma, even though it does not have an upper limit? Should I convert percentages to integer and use Poisson as counts? Should I just stick with Gaussian? I have not found many examples in the literature or in textbooks that try to model percentages in this way. Any hints or insights are appreciated.
Thank you for your answers. In fact, the beta distribution is exactly what I need and is thoroughly discussed in this article:
Eskelson, B. N., Madsen, L., Hagar, J. C., & Temesgen, H. (2011). Estimating Riparian understory vegetation cover with Beta regression and copula models. Forest Science, 57(3), 212-221.
These authors use the betareg package in R by Cribari-Neto and Zeileis.
The following article discusses a good way to transform a beta-distributed response variable when it includes true 0's and/or 1's in the range of percentages:
- Smithson , M., and J. Verkuilen, 2006. A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables, Psychological Methods, 11(1):54–71.