Levy / Mislevy Bayesian Psychometric Modeling

Erscheinungsjahr 2016
ISBN: 978-1-4398-8468-3
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 492 Seiten

Reihe: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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.

Autoren/Hrsg.

Levy, Roy

Mislevy, Robert J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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

Über Autor(innen)

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.