Please visit [https://arxiv.org/abs/2307.10503] for the preprint. The preprint is unblinded. Study 1 is replicable using the R script and Stan model files in the Study 1 folder. A text script within that folder provides details on the R environment and version of packages for when this study was conducted. We do not guarantee that the scripts will work on other version of R or Stan. Study 2 code is provided for how the data were generated, script files were run, and how results were extracted. Replicating this study is very computationally intensive and time consuming. Study 3 using data from the Gallup World Poll on the measurement of Balance and Harmony between the United States and Norway. These analyses are not quite as time consuming but sample sizes were 2000+ cases which can be computationally intensive in Stan for these types of models. Analyses for Study 2 and 3 were conducted using Harvard University's FASRC cannon cluster. The computations in this paper were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University.