Table 1.
Summary of key functions from R packages.
Fig 1.
Testing the Laplace approximation of the random effects.
Bayesian integration was performed on the wildflower TMB model with random effects integrated using two “versions”: (1) the Laplace approximation and (2) full MCMC integration via NUTS. Bayesian posterior samples of selected fixed effects (estimated with NUTS) are shown. Columns and rows corresponds to a fixed effect parameter, with the diagonal showing a QQ-plot of the two versions of the model for that parameter, including a 1:1 line in gray. Lower diagonal plots contain pairwise parameter posterior points, with color corresponding to integration version, and larger colored circles the pairwise medians. Posterior rows were randomized to prevent consistent overplotting of one version. Differences in versions suggest the Laplace approximation assumptions are not met. Other fixed effects showed no differences and are left off for clarity.
Fig 2.
Testing the Laplace approximation integration of the random effects.
Same as for Fig 1 except for three hypervariances and a slope parameter in the swallows model.