Hierarchical Bayes Analysis of Behavioral Experiments
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In this dissertation, we develop generalized hierarchical Bayesian ANOVA, to assist experimental researchers in the behavioral and social sciences in the analysis of the effects of experimentally manipulated within- and between-subjects factors. The method alleviates several limitations of classical ANOVA, still commonly employed in those fields. An accompanying R package for hierarchical Bayesian ANOVA is developed. It offers statistical routines and several easy-to-use functions for esti- mation of hierarchical Bayesian ANOVA models that are tailored to the analysis of experimental research. Markov chain Monte Carlo (MCMC) simulation is used to simulate posterior samples of the parameters of each model specified by the user. The core program of all models is written in R and JAGS (Just Another Gibbs Sam- pler) which is very similar to the famous software WinBUGS. After preparing the data in the required format, users simply select an appropriate model, and estimate it without any advanced coding. The main aim of the R package is to offer freely accessible resources for hierarchical Bayesian ANOVA analysis, which makes it easy to use for behavioral researchers. We also develop generalized Bayesian mediation models for analysis of mediation effects. By using Bayesian analysis, inference is straightforward and exact, which makes it appealing for experimental studies with small samples. The Bayesian approach is also conceptually simpler for any model with a complicated structure, especially for multilevel mediation analysis. Analysis of several data sets are used to illustrate the proposed methods.