Bayesian Statistics for the Social Sciences

by David Kaplan PhD

Overview

The second edition of this practical book equips social science researchers to apply the latest Bayesian methodologies to their data analysis problems. It includes new chapters on model uncertainty, Bayesian variable selection and sparsity, and Bayesian workflow for statistical modeling. Clearly explaining frequentist and epistemic probability and prior distributions, the second edition emphasizes use of the open-source RStan software package. The text covers Hamiltonian Monte Carlo, Bayesian linear regression and generalized linear models, model evaluation and comparison, multilevel modeling, models for continuous and categorical latent variables, missing data, and more. Concepts are fully illustrated with worked-through examples from large-scale educational and social science databases, such as the Program for International Student Assessment and the Early Childhood Longitudinal Study. Annotated RStan code appears in screened boxes; the companion website (www.guilford.com/kaplan-materials) provides data sets and code for the book's examples.
 
New to This Edition
*Utilizes the R interface to Stan—faster and more stable than previously available Bayesian software—for most of the applications discussed.
*Coverage of Hamiltonian MC; Cromwell’s rule; Jeffreys' prior; the LKJ prior for correlation matrices; model evaluation and model comparison, with a critique of the Bayesian information criterion; variational Bayes as an alternative to Markov chain Monte Carlo (MCMC) sampling; and other new topics.
*Chapters on Bayesian variable selection and sparsity, model uncertainty and model averaging, and Bayesian workflow for statistical modeling.
 

Product Details

ISBN-13:	9781462553549
Publisher:	Guilford Publications, Inc.
Publication date:	11/10/2023
Series:	Methodology in the Social Sciences Series
Edition description:	Second Edition
Pages:	250
Product dimensions:	7.00(w) x 10.00(h) x 0.62(d)

About the Author

David Kaplan, PhD, is the Patricia Busk Professor of Quantitative Methods in the Department of Educational Psychology at the University of Wisconsin–Madison and holds affiliate appointments in the University of Wisconsin’s Department of Population Health Sciences, the Center for Demography and Ecology, and the Nelson Institute for Environmental Studies. Dr. Kaplan’s research focuses on the development of Bayesian statistical methods for education research. His work on these topics is directed toward applications to large-scale cross-sectional and longitudinal survey designs. He has been actively involved in the OECD Program for International Student Assessment (PISA), serving on its Technical Advisory Group from 2005 to 2009 and its Questionnaire Expert Group from 2004 to the present, and chairing the Questionnaire Expert Group for PISA 2015. He also serves on the Design and Analysis Committee and the Questionnaire Standing Committee for the National Assessment of Educational Progress. Dr. Kaplan is an elected member of the National Academy of Education and former chair of its Research Advisory Committee, president (2023–2024) of the Psychometric Society, and past president of the Society for Multivariate Experimental Psychology. He is a fellow of the American Psychological Association (Division 5), a former visiting fellow at the Luxembourg Institute for Social and Economic Research, a former Jeanne Griffith Fellow at the National Center for Education Statistics, and a current fellow at the Leibniz Institute for Educational Trajectories in Bamberg, Germany. He is a recipient of the Samuel J. Messick Distinguished Scientific Contributions Award from the American Psychological Association (Division 5), the Alexander von Humboldt Research Award, and the Hilldale Award for the Social Sciences from the University of Wisconsin–Madison. Dr. Kaplan was the Johann von Spix International Visiting Professor at the Universität Bamberg and the Max Kade Visiting Professor at the Universität Heidelberg, both in Germany, and is currently International Guest Professor at the Universität Heidelberg. 

Table of Contents

I. Foundations of Bayesian Statistics
1. Probability Concepts and Bayes' Theorem
1.1. Relevant Probability Axioms
1.1.1. Probability as Long-Run Frequency
1.1.2. The Kolmogorov Axioms of Probability
1.1.3. The Rényi Axioms of Probability
1.1.4. Bayes' Theorem
1.1.5. Epistemic Probability
1.1.6. Coherence
1.2. Summary
1.3. Suggested Readings
2. Statistical Elements of Bayes' Theorem
2.1. The Assumption of Exchangeability
2.2. The Prior Distribution
2.2.1. Noninformative Priors
2.2.2 .Informative Priors
2.3. Likelihood
2.3.1. The Law of Likelihood
2.4. The Posterior Distribution
2.5. The Bayesian Central Limit Theorem and Bayesian Shrinkage
2.6. Summary
2.7. Suggested Readings
2.8. Appendix 2.1. Derivation of Jeffreys' Prior
3. Common Probability Distributions
3.1. The Normal Distribution
3.1.1. The Conjugate Prior for the Normal Distribution
3.2. The Uniform Distribution
3.2.1. The Uniform Distribution as a Noninformative Prior
3.3. The Poisson Distribution
3.3.1. The Gamma Density: Conjugate Prior for the Poisson Distribution
3.4. The Binomial Distribution
3.4.1. The Beta Distribution: Conjugate Prior for the Binomial Distribution
3.5. The Multinomial Distribution
3.5.1. The Dirichlet Distribution: Conjugate Prior for the Multinomial Distribution
3.6. The Wishart Distribution
3.6.1. The Inverse-Wishart Distribution: Conjugate Prior for the Wishart Distribution
3.7. Summary
3.8. Suggested Readings
3.9. Appendix 3.1. R Code for Chapter 3
4. Markov Chain Monte Carlo Sampling
4.1. Basic Ideas of MCMC Sampling
4.2. The Metropolis–Hastings Algorithm
4.3. The Gibbs Sampler
4.4. Convergence Diagnostics
4.5. Summary
4.6. Suggested Readings
4.7. Appendix 4.1. R Code for Chapter 4
II. Topics in Bayesian Modeling
5. Bayesian Hypothesis Testing
5.1. Setting the Stage: The Classical Approach to Hypothesis Testing and Its Limitations
5.2. Point Estimates of the Posterior Distribution
5.2.1. Interval Summaries of the Posterior Distribution
5.3. Bayesian Model Evaluation and Comparison
5.3.1. Posterior Predictive Checks
5.3.2. Bayes Factors
5.3.3. The Bayesian Information Criterion
5.3.4. The Deviance Information Criterion
5.4. Bayesian Model Averaging
5.4.1 Occam's Window
5.4.2. Markov Chain Monte Carlo Model Composition
5.5. Summary
5.6. Suggested Readings
6. Bayesian Linear and Generalized Linear Models
6.1. A Motivating Example
6.2. The Normal Linear Regression Model
6.3. The Bayesian Linear Regression Model
6.3.1. Noninformative Priors in the Linear Regression Model
6.3.2. Informative Conjugate Priors
6.4. Bayesian Generalized Linear Models
6.4.1. The Link Function
6.4.2. The Logit-Link Function for Logistic and Multinomial Models
6.5 Summary
6.6 Suggested Readings
6.7. Appendix 6.1. R Code for Chapter 6
7. Missing Data from a Bayesian Perspective
7.1. A Nomenclature for Missing Data
7.2. Ad Hoc Deletion Methods for Handling Missing Data
7.2.1. Listwise Deletion
7.2.2. Pairwise Deletion
7.3. Single Imputation Methods
7.3.1. Mean Imputation
7.3.2. Regression Imputation
7.3.3. Stochastic Regression Imputation
7.3.4. Hot-Deck Imputation
7.3.5. Predictive Mean Matching
7.4. Bayesian Methods of Multiple Imputation
7.4.1. Data Augmentation
7.4.2. Chained Equations
7.4.3. EM Bootstrap: A Hybrid Bayesian/Frequentist Method
7.4.4. Bayesian Bootstrap Predictive Mean Matching
7.5. Summary
7.6. Suggested Readings
7.7. Appendix 7.1. R Code for Chapter 7
III. Advanced Bayesian Modeling Methods
8. Bayesian Multilevel Modeling
8.1 Bayesian Random Effects Analysis of Variance
8.2. Revisiting Exchangeability
8.3. Bayesian Multilevel Regression
8.4. Summary
8.5. Suggested Readings
8.6. Appendix 8.1. R Code for Chapter 8
9. Bayesian Modeling for Continuous and Categorical Latent Variables
9.1. Bayesian Estimation of the CFA Model
9.1.1. Conjugate Priors for CFA Model Parameters
9.2. Bayesian SEM
9.2.1. Conjugate Priors for SEM Parameters
9.2.2. MCMC Sampling for Bayesian SEM
9.3. Bayesian Multilevel SEM
9.4. Bayesian Growth Curve Modeling
9.5. Bayesian Models for Categorical Latent Variables
9.5.1. Mixture Model Specification
9.5.2. Bayesian Mixture Models
9.6. Summary
9.7. Suggested Readings
9.8. Appendix 9.1. “RJAGS” Code for Chapter 9
10. Philosophical Debates in Bayesian Statistical Inference
10.1. A Summary of the Bayesian Versus Frequentist Schools of Statistics
10.1.1. Conditioning on Data
10.1.2. Inferences Based on Data Actually Observed
10.1.3. Quantifying Evidence
10.1.4. Summarizing the Bayesian Advantage
10.2. Subjective Bayes
10.3. Objective Bayes
10.4. Final Thoughts: A Call for Evidence-Base Subjective Bayes
References
Index

Interviews

Behavioral and social science researchers; instructors and graduate students in psychology, education, sociology, management, and public health. Will serve as a core book for courses on Bayesian or advanced quantitative techniques.

Editorial Reviews

"This very practical book is well suited to social science students because of the examples used (large-scale surveys) and the coverage of methods that social scientists often need (latent variables, variable selection, and dealing with missing data). The book also covers some topics readers may not know they need—Bayesian model averaging and workflow, for example. Illustrations use RStan, perhaps the most flexible of programs for Bayesian modeling. Full integration of RStan input and output is provided in the text."—David Rindskopf, PhD, Distinguished Professor of Educational Psychology and Psychology, The Graduate Center, The City University of New York

"Kaplan's book is the perfect follow-up for those whose curiosity has been piqued about Bayesian statistics. The many code examples will give users a head start for applying Bayes' theorem to their data. I highly appreciate that the author uses open-source software for all models. The topics are introduced with a rich amount of background information, some equations (but never too many), detailed explanations, and code examples. Empirical results are used to illustrate each topic."—Rens van de Schoot, PhD, Department of Methodology and Statistics, Utrecht University, Netherlands

"An excellent resource for researchers at the graduate level or above with an interest in Bayesian statistics. Readers are skillfully guided through the process of statistical reasoning from a Bayesian perspective. This book is practical and minimally technical while also introducing readers to interesting historical and philosophical issues. What makes the book especially helpful is Kaplan’s careful balance of breadth and depth of coverage of key topics. In this timely second edition, important recent advances in Bayesian statistics are distilled and disseminated for researchers in the social sciences."—Sierra A. Bainter, PhD, Department of Psychology, University of Miami

"This book has all the essential components to help readers, especially quantitative researchers in social sciences, understand and conduct Bayesian modeling. The second edition includes new material on recent Markov chain Monte Carlo (MCMC) methods, such as Hamiltonian MC, in addition to a range of other updates."—Insu Paek, PhD, Senior Scientist, Human Resources Research Organization

"I recommend this book for providing a careful overview of the Bayesian framework, at a level accessible to a wide audience, with examples, code, and key references. Kaplan does a great job of covering so many different aspects of Bayesian modeling in a coherent way and presenting a number of substantive methods for analyzing complex data. I liked the comparisons and analogies to the frequentist approach."—Irini Moustaki, PhD, Department of Statistics, London School of Economics and Political Science, United Kingdom

From the Publisher

"A valuable read for researchers, practitioners, teachers, and graduate students in the field of social sciences….Extremely accessible and incredibly delightful….The wide breadth of topics covered, along with the author’s clear and engaging style of writing and inclusion of numerous examples, should provide an adequate foundation for any psychologist wishing to take a leap into Bayesian thinking. Furthermore, the technical details and analytic aspects provided in all chapters should equip readers with enough knowledge to embark on Bayesian analysis with their own research data.” (on the first edition)

Psychometrika