Ecological Archives E096-096-A2
Chris H. Wilson, T. Trevor Caughlin, David J. Civitello, and S. Luke Flory. 2015. Combining mesocosm and filed experiments to predict invasive plant performance: a hierarchical Bayesian approach. Ecology 96:1084–1092. http://dx.doi.org/10.1890/14-0797.1
Appendix B. Simulation test of the gamma-gamma hierarchical biomass model.
We created fake data by generating a random vector of 20 light levels between 1–100%. Then, each light level was assigned to a Michaelis-Menten function to determine the mean of a gamma-distributed variable. We thus created 20 site means. Within each site mean, we sampled 20 random individual biomass observations, for a total of 400 datapoints. We re-fit our hierarchical model with this data set, and plotted the posterior predictive distribution against the fake data-points. The good fit of our model (including reasonably accurate estimation of the Michaelis-Menten parameters used to simulate the site means), confirms that: (a) our model is correctly specified and (b) our real data set (n = 381 biomass observations) is sufficiently large to parameterize this model.
Fig. B1. Simulation test of gamma-gamma hierarchical biomass model. Red line is the mean prediction, and the dashed blue lines are probability contours enclosing a 95% credible interval.