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Bayesian Psychometric Modeling




ISBN 9781439884676
Published May 23, 2016 by Chapman and Hall/CRC
466 Pages - 88 B/W Illustrations

 
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Book Description

A Single Cohesive Framework of Tools and Procedures for Psychometrics and Assessment

Bayesian Psychometric Modeling presents a unified Bayesian approach across traditionally separate families of psychometric models. It shows that Bayesian techniques, as alternatives to conventional approaches, offer distinct and profound advantages in achieving many goals of psychometrics.

Adopting a Bayesian approach can aid in unifying seemingly disparate—and sometimes conflicting—ideas and activities in psychometrics. This book explains both how to perform psychometrics using Bayesian methods and why many of the activities in psychometrics align with Bayesian thinking.

The first part of the book introduces foundational principles and statistical models, including conceptual issues, normal distribution models, Markov chain Monte Carlo estimation, and regression. Focusing more directly on psychometrics, the second part covers popular psychometric models, including classical test theory, factor analysis, item response theory, latent class analysis, and Bayesian networks. Throughout the book, procedures are illustrated using examples primarily from educational assessments. A supplementary website provides the datasets, WinBUGS code, R code, and Netica files used in the examples.

Table of Contents

Foundations
Overview of Assessment and Psychometric Modeling

Assessment as Evidentiary Reasoning
The Role of Probability
The Role of Context in the Assessment Argument
Evidence-Centered Design
Summary and Looking Ahead

Introduction to Bayesian Inference
Review of Frequentist Inference via Maximum Likelihood
Bayesian Inference
Bernoulli and Binomial Models
Summarizing Posterior Distributions
Graphical Model Representation
Analyses Using WinBUGS
Summary and Bibliographic Note
Exercises

Conceptual Issues in Bayesian Inference
Relative Influence of the Prior Distribution and the Data
Specifying Prior Distributions
Comparing Bayesian and Frequentist Inferences and Interpretations
Exchangeability, Conditional Independence, and Bayesian Inference
Why Bayes?
Conceptualizations of Bayesian Modeling
Summary and Bibliographic Note

Normal Distribution Models
Model with Unknown Mean and Known Variance
Model with Known Mean and Unknown Variance
Model with Unknown Mean and Unknown Variance
Summary
Exercises

Markov Chain Monte Carlo Estimation
Overview of MCMC
Gibbs Sampling
Metropolis Sampling
How MCMC Facilitates Bayesian Modeling
Metropolis–Hastings Sampling
Single-Component-Metropolis or Metropolis-within-Gibbs Sampling
Practical Issues in MCMC
Summary and Bibliographic Note
Exercises

Regression
Background and Notation
Conditional Probability of the Data
Conditionally Conjugate Prior
Complete Model and Posterior Distribution
MCMC Estimation
Example: Regressing Test Scores on Previous Test Scores
Summary and Bibliographic Note
Exercises

Psychometrics
Canonical Bayesian Psychometric Modeling

Three Kinds of DAGs
Canonical Psychometric Model
Bayesian Analysis
Bayesian Methods and Conventional Psychometric Modeling
Summary and Looking Ahead
Exercises

Classical Test Theory
CTT with Known Measurement Model Parameters and Hyperparameters, Single Observable (Test or Measure)
CTT with Known Measurement Model Parameters and Hyperparameters, Multiple Observables (Tests or Measures)
CTT with Unknown Measurement Model Parameters and Hyperparameters
Summary and Bibliographic Note
Exercises

Confirmatory Factor Analysis
Conventional Factor Analysis
Bayesian Factor Analysis
Example: Single Latent Variable (Factor) Model
Example: Multiple Latent Variable (Factor) Model
CFA Using Summary Level Statistics
Comparing DAGs and Path Diagrams
A Hierarchical Model Construction Perspective
Flexible Bayesian Modeling
Latent Variable Indeterminacies from a Bayesian Modeling Perspective
Summary and Bibliographic Note
Exercises

Model Evaluation
Interpretability of the Results
Model Checking
Model Comparison
Exercises

Item Response Theory
Conventional Item Response Theory Models for Dichotomous Observables
Bayesian Modeling of Item Response Theory Models for Dichotomous Observables
Conventional Item Response Theory Models for Polytomous Observables
Bayesian Modeling of Item Response Theory Models for Polytomous Observables
Multidimensional Item Response Theory Models
Illustrative Applications
Alternative Prior Distributions for Measurement Model Parameters
Latent Response Variable Formulation and Data-Augmented Gibbs Sampling
Summary and Bibliographic Note
Exercises

Missing Data Modeling
Core Concepts in Missing Data Theory
Inference under Ignorability
Inference under Nonignorability
Multiple Imputation
Latent Variables, Missing Data, Parameters, and Unknowns
Summary and Bibliographic Note
Exercises

Latent Class Analysis
Conventional Latent Class Analysis
Bayesian Latent Class Analysis
Bayesian Analysis for Dichotomous Latent and Observable Variables
Example: Academic Cheating
Latent Variable Indeterminacies from a Bayesian Modeling Perspective
Summary and Bibliographic Note
Exercises

Bayesian Networks
Overview of Bayesian Networks
Bayesian Networks as Psychometric Models
Fitting Bayesian Networks
Diagnostic Classification Models
Bayesian Networks in Complex Assessment
Dynamic Bayesian Networks
Summary and Bibliographic Note
Exercises

Conclusion
Bayes as a Useful Framework
Some Caution in Mechanically (or Unthinkingly) Using Bayesian Approaches
Final Words

Appendix A: Full Conditional Distributions
Appendix B: Probability Distributions

References

Index

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Author(s)

Biography

Roy Levy is an associate professor of measurement and statistical analysis in the T. Denny Sanford School of Social and Family Dynamics at Arizona State University. His primary research and teaching interests include methodological developments and applications of psychometrics and statistics to assessment, education, and the social sciences. He has received awards from the President of the United States, Division D of the American Educational Research Association, and the National Council on Measurement in Education.

Robert J. Mislevy is the Frederic M. Lord Chair in Measurement and Statistics at Educational Testing Service. He was previously a professor of measurement and statistics at the University of Maryland and an affiliated professor of second language acquisition and survey methodology. His research applies developments in statistics, technology, and psychology to practical problems in assessment, including the development of multiple-imputation analysis in the National Assessment of Educational Progress. He is a member of the National Academy of Education and has been a president of the Psychometric Society. He has received awards from the National Council on Measurement in Education and Division D of the American Educational Research Association.

Reviews

"One true asset of this book is the impeccable organization. The topics build upon one another nicely, with the most basic of models (i.e., the true score model) presented first. The flow of the chapters was well designed, with model complexity increasing steadily through the topics. The authors introduced latent variable modeling using continuous latent variables (e.g., confirmatory factor analysis and item response theory). Then, they extended this idea into the incorporation of categorical latent variables (e.g., latent class modeling and Bayes networks). Within each chapter, the most common priors were presented and described for each model. The description and illustration of implementing priors for continuous and categorical latent variable models were done particularly well…The authors successfully incorporated examples throughout the entire text. These examples were quite detailed and included everything from model specification, annotated software syntax, diagnostics, results, and interpretation. Many examples use publicly available data. Not only does this feature make replication possible for the results, but it is also an added benefit for students using this as a course textbook. One could easily walk through the steps in this book and conduct analyses from all of the model-based chapters included...Given the strong emphasis on examples and detailed descriptions throughout the book, we highly recommend this as a textbook for graduate-level courses on Bayesian statistics or psychometrics. The authors effectively balanced the content regarding general Bayesian inference and specific psychometric models. Therefore, the book can be used as either the main text for a standalone course on Bayesian psychometrics or as supplementary reading for a course focusing on a particular model (e.g., factor analysis)."
—Sarah Depaoli and Yang Liu in Psychometrika, June 2018

"This book is a great contribution to the field of Bayesian psychometrics. It provides an excellent introduction to the Bayesian statistical philosophy and the Bayesian way of thinking, with a focus on building statistical models for psychometric analysis. In a clear manner, it describes how Bayesian theory can be used to construct psychometric models and carry out statistical analysis, whilst explaining how to integrate prior knowledge into analysis. It also shows the various profound advantages of the Bayesian approach, and presents a comprehensive toolbox for psychometric data analysis, as opposed to conventional approaches.
This book is highly recommended for graduate students and (applied) researchers, who have a basic understanding of psychometric and statistical theory. The second part of the book contains a wide overview of different psychometric models and theories such as classical test theory, item response theory, latent class analysis, and Bayesian networks. A clear and consistent Bayesian approach introduces these different topics, which are illustrated with educational assessment applications. In addition to several programs in R, the WinBUGS program is also utilised to perform computations, making it possible to directly apply the presented material. Overall, this book provides a thorough and comprehensive overview of psychometric modelling, and truly promotes the use of Bayesian methods."
Jean-Paul Fox, Department of Research Methodology, Measurement and Data Analysis, University of Twente

"Drs. Roy Levy and Robert Mislevy have made several pioneering contributions on the application of Bayesian statistical analysis to educational and psychological measurements, and have now brought their expertise to life in the accessible, up-to-date, and comprehensive book Bayesian Psychometric Modeling. This is a must-read for researchers and practitioners of all levels, from undergraduate students of Psychology or Education to experts on Bayesian psychometrics. A unique aspect of the book is its descriptions of the connections between Bayesian modelling and topics such as evidence-centred design and graphical models, which are the authors’ forte. This book provokes the reader into thinking deeper about the topic and is destined to become a classic for those who are interested in the area."
Sandip Sinharay, Principal Research Scientist, Educational Testing Service (ETS)

"The last couple of decades has seen a widening of the gap between psychometrics as taught in textbooks and psychometrics as practiced in industry-leading agencies, with the latter expanding rapidly due to increasingly sophisticated assessment needs and increasingly accessible computational power. Bayesian Psychometric Modeling helps to close this gap, using a model-based and evidentiary reasoning perspective to frame psychometrics as part of a larger landscape methodologically, statistically, computationally, and philosophically. Levy and Mislevy are that rare combination of outstanding scholars and teachers, and it comes through beautifully in their exemplary treatments of not just standard topics like classical test theory and item response theory, but also of Bayesian inference, graph theory, MCMC estimation, model evaluation, confirmatory factor analysis, multidimensional IRT models, latent class analysis, and Bayesian networks. Truly modern psychometrics demands flexible and integrated thinking, and analytical frameworks to match. This book embodies such thinking and analysis, representing where the leaders are and where the rest of us should be going. And it helps us to get there."
Gregory R. Hancock, Professor and Program Director of Measurement, Statistics and Evaluation, University of Maryland

"This book is excellent; it is the most comprehensive and up-to-date resource for researchers who are studying, or would like to know more about, Bayesian approaches for psychometric and statistical models. It thoroughly covers simple to advanced topics on psychometric models with mathematical and underlying psychometric concepts, with clear illustrations on a wide range of applications using real data in the psychometric field. Not only useful for its theoretical aspects on Bayesian approaches, the technical parts of this text (e.g., annotated software codes that can be easily modified) are also illustrated in an accessible manner for students, applied statisticians, and psychometricians who may want to apply these techniques to their own problems. If you want to use or find out more about Bayesian psychometric approaches, whether it be those at the simplest level or those at the cutting-edge of theoretical research and practical application, then this is the book for you!"
Jaehwa Choi, Assessment, Testing, and Measurement Program, The George Washington University

"I can honestly say that the book Bayesian Psychometric Modeling by Roy Levy and Robert Mislevy represents a tremendous amount of effort, dedication, and care in the service of rigorous professional development for colleagues who need to educate themselves on principled evidentiary reasoning using Bayesian methodologies. While reading, I was constantly amazed how I was (re)learning both foundational and complex statistical concepts while almost "incidentally" expanding my intellectual horizon through reflection on core principles of evidentiary reasoning. Throughout the book, the intellectual thoughtfulness of the authors shines through in innumerable ways, especially in the way they express ideas and structure the presentation of information. They utilize a broad array of diverse representations (textual descriptions, examples, and anecdotes along with formulas, tables, graphics, and code) that are well-suited for their communicative function, often in interesting novel ways that provide true insight into a phenomenon. Thus, rather than serving as just a vehicle for learning about best statistical practices in Bayesian modeling, the book can really serve to develop intellectual stewardship for future voices in educational measurement that transcends this transcends this particular intellectual domain."
André A. Rupp, Educational Testing Service (ETS)

"This book covers a range of models and ideas in psychometrics and should be of interest to many students and researchers."
Andrew Gelman, Departments of Statistics and Political Science, Columbia University