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I am attempting to model the effect of several continuous and categorical predictors on a continuous proportion response variable. My experiment had 3 treatments, which were replicated in each of 9 plots, in each of two seasons. My response variable was "percentage of total weight that is body fat." Weight is variable between organisms, so I need to use proportions. One of my predictors is "total body weight." I was previously modeling these data incorrectly with a GLMM, using the cbind() function to create a matrix for the components of my proportions. It seems that a beta regression is what I should actually be using. My problem is that I would like to include "source plot" as a random effect. Should I instead just make "source plot" another categorical predictor in the beta regression? If source plot has an effect, how can I remove it see the relative effects between each of the three treatments within every source plot? Should source plot be nested within season?

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  • you could use glmmADMB or glmmTMB (on Github) to fit a Beta model with a random effect of plot
  • you could go ahead and treat plot as a fixed effect (conservative)
  • you could do a boxplot of the residuals from the simple (plot-ignoring) model by source plot, and argue that the among-source-plot variation is small/unimportant
  • you could logistic- or arcsin-sqrt-transform your response to stabilize variance/improve Normality and use a linear mixed model
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  • $\begingroup$ Thank you so much for the response Dr. Bolker. I think I will try to treat plot as a fixed effect in the beta regression, and see how that turns out. $\endgroup$ – betareggedout Aug 16 '15 at 20:09

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