Page 254 - Demo

Appendices252Appendix G: model stability checksIn this appendix, I strive to provide extra information about the model checks that I performed across the empirical chapters in order to assess model stability. First, I will give some context with regard to the WAMBS-checklist (Depaoli & van der Schoot, 2017) that was used to test for model convergence issues throughout the thesis, posterior predictive checks based on the posterior distribution and cross-validation, and Pareto smoothed importance sampling for identification of influential cases (Vehtari et al., 2017). Second, I will provide posterior predictive checks and diagnostics about influential observations for each empirical chapter.Model convergenceWhile relatively simple Bayesian models can rely on methods like grid approximation to estimate the posterior distribution, such methods quickly become computationally costly in the context of multidimensional models that require the approximation of joint posterior distributions (Kruschke, 2014; Johnson et al., 2022). One solution that has gained traction is the use of algorithms such as MCMC (Markov chain Monte Carlo) sampling. Such algorithms provide a useful tool to approximate complex multidimensional posterior distributions rather efficiently by generating values from the posterior distribution via randomly ‘walking’ through the parameter space combined with simple decision rules (Kruschke, 2014). Johnsen et al. (2022) provide an excellent explanation of and tutorial on MCMC sampling.Although MCMC algorithms have provided most useful for Bayesian inference, their usefulness depends strongly on the accuracy and stability of the process. Therefore, it is essential to throughly examine the posterior samples and the stochastics of the algorithm. The WAMBS checklist (Depaoli & van der Schoot, 2017) provides some useful criteria to evaluate these sources of information. First, one can check whether the models converged properly by visually evaluating the trace plots for all four chains for all parameters in the model. By visually inspecting the plots, it is possible to identify divergent transitions, slow mixing within a chain, or chains getting stuck on one particular value. All these issues can result in poor approximation of the posterior distribution (Johnsen et al., 2022). Second, one can visually check the autocorrelation between consecutive iterations within a chain. Although consecutive iterations are by definition autocorrelated to some extent, extreme degrees of autocorrelation can indicate estimation problems within the model (Depaoli & van der Schoot, 2017). Third, one can visually check Tom Roth.indd 252 08-01-2024 10:42