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Symposium on New Developments in Bayesian Analysis at APS 2014

Bayesian methods are becoming increasingly popular and important in psychological science. This symposium covers a wide range of recent topics in Bayesian analysis, including Bayesian meta-analysis, Bayesian power analysis, Bayesian model selection, and semiparametric Bayesian analysis. Applications of the methods are illustrated through real-data analysis.

Bayesian methods have been well established and are becoming increasingly popular in the psychological literature since their introduction to psychology by Edwards, Lindman, and Savage (1963). Nowadays, Bayesian methods have been applied in a large variety of models such as mediation analysis and moderation analysis (e.g., Wang & Zhang, 2011; Wang & Preacher, in press), structural equation models (e.g., Scheines, Hoijtink, & Boomsma, 1999; Muthen & Asparouhov, 2012), growth curve models (e.g., Zhang et al., 2007; 2013), and growth mixture models (e.g., Lu, Zhang, & Lubke, 2011; Lu & Zhang, in press).

The symposium consists of 4 recent studies on Bayesian analysis. The first study discusses how to conduct Bayesian meta-analysis using power prior. In traditional meta-analysis, each study contributes equally to the estimated overall effect. However, this often causes problem. For example, meta-analysis may involve studies from both controlled experiments and sample surveys where the experiment studies can be limited by sample sizes while surveys not. Therefore, survey studies can easily dominate meta-analysis. The proposed Bayesian meta-analysis can control the contribution of individual study through power prior. Bayesian methods are developed for both fixed-effects and random-effects meta-analysis as well as meta-regression. Online software is provided to carry out the proposed Bayesian meta-analysis.

The second study proposes to conduct power analysis through Bayesian methods by allowing uncertainty in the population effect size. Traditional power analysis typically assumes that effect size can only take a given value. In real studies, researchers are often not 100% sure about the effect size for a prospective power analysis. Instead, a range of plausible values is suspected to reflect researchers’ uncertainty about the effect size. This study discusses how to conduct power analysis with uncertainty in effect sizes via various frequentist and Bayesian methods. Ideas of each method will be introduced and power results from applying different methods to (1) compare independent group means and (2) test mediation effects will be compared and discussed.

The third study aims to investigate the performance of the Bayesian model selection criteria with general Latent growth curve modeling models, such as non-normally distributed growth models, growth mixture models, and extended growth mixture models. Latent growth modeling is becoming increasingly important in psychological, social, and educational research. As estimates from mis-specified models may lead to severely misleading conclusions, it is necessary to compare several competing models and identify the best-fit one. Both simulation studies and real data analysis are used to comparably evaluate several proposed model selection criteria.

The fourth study deals with a practical issue of longitudinal data analysis – nonnormality of data – through semeparametric Bayesian methods. Four types of distributional growth curve models are proposed, in which random coefficients or measurement errors follow either normal distributions or unknown distributions with Dirichlet priors. After demonstrating their performances for different types of data, we present several methods to select an appropriate model for real data analysis. Both simulation studies and real data analysis are used to illustrate the application of robust semiparametric growth curve models.

Bayesian meta-analysis of correlation through power prior

Zhiyong Zhang

University of Notre Dame

Co-Author: Kaifeng Jiang, University of Notre Dame

Co-Author: Haiyan Liu, University of Notre Dame

Power analysis with uncertainty in effect sizes

Lijuan Wang

University of Notre Dame

Co-Author: Han Du, University of Notre Dame

Bayesian Model Selection Criteria for Latent Growth Models

Zhenqiu Lu

University of Georgia

Robust semiparametric Bayesian methods in growth curve modeling with nonnormal data

Xin Tong

University of Notre Dame

Co-Author: Zhiyong Zhang, University of Notre Dame

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