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.