Bayesian Evaluation of Informative Hypotheses

1. Front Matter

   Pages I-XI

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2. An Introduction to Bayesian Evaluation of Informative Hypotheses

   1. Front Matter

      Pages 1-1

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   2. An Introduction to Bayesian Evaluation of Informative Hypotheses

      • Herbert Hoijtink, Irene Klugkist, Paul A. Boelen

      Pages 1-3

3. Bayesian Evaluation of Informative Hypotheses

   1. Front Matter

      Pages 5-5

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   2. Illustrative Psychological Data and Hypotheses for Bayesian Inequality Constrained Analysis of Variance

      • Paul A. Boelen, Herbert Hoijtink

      Pages 7-26

   3. Bayesian Estimation for Inequality Constrained Analysis of Variance

      • Irene Klugkist, Joris Mulder

      Pages 27-52

   4. Encompassing Prior Based Model Selection for Inequality Constrained Analysis of Variance

      • Irene Klugkist

      Pages 53-83

   5. An Evaluation of Bayesian Inequality Constrained Analysis of Variance

      • Herbert Hoijtink, Rafaele Huntjens, Albert Reijntjes, Rebecca Kuiper, Paul A. Boelen

      Pages 85-108

4. A Further Study of Prior Distributions and the Bayes Factor

   1. Front Matter

      Pages 109-109

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   2. Bayes Factors Based on Test Statistics Under Order Restrictions

      • David Rossell, Veerabhadran Baladandayuthapani, Valen E. Johnson

      Pages 111-129

   3. Objective Bayes Factors for Informative Hypotheses: “Completing” the Informative Hypothesis and “Splitting” the Bayes Factors

      • Luis Raúl Pericchi Guerra, Guimei Liu, David Torres Núñez

      Pages 131-154

   4. The Bayes Factor Versus Other Model Selection Criteria for the Selection of Constrained Models

      • Ming-Hui Chen, Sungduk Kim

      Pages 155-180

   5. Bayesian Versus Frequentist Inference

      • Eric-Jan Wagenmakers, Michael Lee, Tom Lodewyckx, Geoffrey J. Iverson

      Pages 181-207

5. Beyond Analysis of Variance

   1. Front Matter

      Pages 209-209

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   2. Inequality Constrained Analysis of Covariance

      • Irene Klugkist, Floryt van Wesel, Sonja van Well, Annemarie Kolk

      Pages 211-225

   3. Inequality Constrained Latent Class Models

      • Herbert Hoijtink, Jan Boom

      Pages 227-246

   4. Inequality Constrained Contingency Table Analysis

      • Olav Laudy

      Pages 247-271

   5. Inequality Constrained Multilevel Models

      • Bernet Sekasanvu Kato, Carel F.W. Peeters

      Pages 273-295

6. Evaluations

   1. Front Matter

      Pages 297-297

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   2. A Psychologist’s View on Bayesian Evaluation of Informative Hypotheses

      • Marleen Rijkeboer, Marcel van den Hout

      Pages 299-308

This book provides an overview of the developments in the area of Bayesian evaluation of informative hypotheses that took place since the publication of the ?rst paper on this topic in 2001 [Hoijtink, H. Con?rmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563–588]. The current state of a?airs was presented and discussed by the authors of this book during a workshop in Utrecht in June 2007. Here we would like to thank all authors for their participation, ideas, and contributions. We would also like to thank Sophie van der Zee for her editorial e?orts during the construction of this book. Another word of thanks is due to John Kimmel of Springer for his con?dence in the editors and authors. Finally, we would like to thank the Netherlands Organization for Scienti?c Research (NWO) whose VICI grant (453-05-002) awarded to the ?rst author enabled the organization of the workshop, the writing of this book, and continuation of the research with respect to Bayesian evaluation of informative hypotheses.

• Evaluation
• Latent Class Analysis
• analysis of variance
• multilevel analysis
• statistics

From the reviews:

“While this book is a collection of papers, the editors have done a great service to the reader by choosing three substantial psychology research studies that are used as examples throughout the book. The continuity of examples provides easy comparison among the methods and makes subsequent developments easier to follow. The book identifies open questions…and provides alternative methodologies with discussion. Each chapter provides a comprehensive bibliography, which makes this book an excellent reference. Statisticians and quantitative social scientists who are interested in a broad introduction and review of Bayesian methods for informative hypotheses, including several chapters of detailed statistical development, will find this book valuable.” (Journal of the American Statistical Association, Mar. 2010, Vol. 105, No.489)

“…Bayesian evaluation for informative hypotheses was first proposed by Hoijtink (2001). The present book collects the recent developments in the area… since then. The content…is the result of written contributions from the workshop in Utrecht in June 2007. …The book is well written … software accompanying the main topics... are available on the website. …This book is motivated largely by a number of examples in psychological and social science, resulting in the particular interest to the researchers in these fields. However researchers in other disciplines such as public health and biomedical science may find this book useful since similar questions of informative hypotheses are encountered frequently in those fields as well. The book succeeds in its aims and is undoubtedly a valuable resource for the public. I would recommend the book to psychologists and scientists in the aforementioned areas who wish to do more complicated analyses. I would also recommend this book to biostatisticians and statisticians who are keen to expand their horizons orwant to attain some inspiration… .” (Biometrics 65, 1308–1309, December 2009)

"This book has been very imaginatively planned and anchored around analysis of challenging problems of (Clinical) Psychology. Not only the analyses but the design of experiments and the variables measured are very interesting. ... This is an excellent book for psychologists and Bayesian statisticians. Strongly recommended for both categories of readers." (International Statistical Review 2009, 77, 2)

“The methods developed here are applicable in areas other than ANOVA, such as ANCOVA, latent class models, and contingency tables. … For those who find ANOVA troubling … and are not so devoted to frequentist approaches as to be troubled by the use of priors (informative or not), this book provides a way forward. If you fall into this class of readers, I highly recommend that you read this book and, when appropriate, consider using the methods described therein in your own work.” (Lawrence Barker, Technometrics, Vol. 52 (3), August, 2010)

• Department of Methods and Statistics, Faculty of Social Sciences, University of Utrecht, Utrecht, The Netherlands

  Herbert Hoijtink, Irene Klugkist

• Department of Clinical and Health Psychology, Faculty of Social Sciences, University of Utrecht, Utrecht, The Netherlands

  Paul A. Boelen

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