Bayesian Psychometric Modeling

Appendix A: Full Conditional Distributions

We develop the full conditional distributions for regression (Chapter 6), CTT (Chapter 8), CFA (Chapter 9), IRT (Chapter 11), and LCA (Chapter 13) models in Sections A.1, A.2, A.3, A.4, A.5, respectively. For each model, we restate the posterior distribution and then pursue the full conditionals. For completeness and transparency in the full conditionals, we expand beyond what was presented in the chapters to include conditioning on the hyperparameters. When the hyperparameters are specified in advance, they are not random variables in the sense of other model parameters and the data. However, including them serves to highlight that they are involved in the computations and aligns with the use of expanded ...