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Appendices253Athe histograms of the posterior distributions for each parameter for gaps or other abnormalities. In most cases, the posterior distributions are expected to be smooth and follow a Gaussian distribution, with one exception being variance parameters that are zero-bounded. Fourth, to investigate the similarity between separate chains, one can examine the Gelman-Rubin statistic (Gelman & Rubin, 1992). This statistic compares the within-chain variability to the between-chain variability. If between-chain variance is relatively small compared to withinchain variance -which is indicative of a well-converged model- the Gelman-Rubin diagnostic for a parameter should be close to 1, and at least not larger than 1.1 (Gelman & Rubin, 1992). The brms-package incorporates an adapted version of the Gelman-Rubin diagnostic, that is reported as the Rhat (Vehtari et al., 2021). For all Bayesian regression models reported in this thesis, the abovementioned steps were taken to ensure correct convergence of the models. I identified no convergence issues in any of the models reported. Therefore, in the remainder of this appendix, I will not report the specific diagnostics per model.Posterior predictive checksNext to convergence, there are other aspects of Bayesian regression models that are important to check, such as the predictive validity of the model. If a model fits well to the data, it should be able to predict new data from this model that are relatively similar to our original data (Johnsen et al., 2022; Kruschke, 2014). It is important to note that this is a different question from model convergence: a well-converged model can have a poor fit to the underlying data. For example, one can easily fit a converging Gaussian regression model to extremely zeroinflated data, and -despite the convergence- predictions based on the model will deviate strongly from the underlying data, indicating model misspecification.One way to test whether the model fits the original data well is performing visual checks of the posterior predictive distribution. This can be done by creating graphs that plot the distribution of the original data on top of the distributions based on multiple simulated datasets randomly drawn from the posterior predictive distribution (Gabry et al., 2019). If the model fits the original data well, we expect the distribution of the original data to overlap with the distributions of simulated datasets. However, if this is not the case, the model is potentially misspecified, either because important predictors are missing or because the error distribution of the model does not fit the data well (Johnsen et al., 2022). Therefore, I will report posterior predictive checks for the main models reported in the empirical chapters.Tom Roth.indd 253 08-01-2024 10:42