1st Edition
Measurement Models for Psychological Attributes
Despite the overwhelming use of tests and questionnaires, the psychometric models for constructing these instruments are often poorly understood, leading to suboptimal measurement. Measurement Models for Psychological Attributes is a comprehensive and accessible treatment of the common and the less than common measurement models for the social, behavioral, and health sciences. The monograph explains the adequate use of measurement models for test construction, points out their merits and drawbacks, and critically discusses topics that have raised and continue to raise controversy. Because introductory texts on statistics and psychometrics are sufficient to understand its content, the monograph may be used in advanced courses on applied psychometrics and is attractive to both researchers and graduate students in psychology, education, sociology, political science, medicine and marketing, policy research, and opinion research.
The monograph provides an in-depth discussion of classical test theory and factor models in Chapter 2; nonparametric and parametric item response theory in Chapter 3 and Chapter 4, respectively; latent class models and cognitive diagnosis models in Chapter 5; and discusses pairwise comparison models, proximity models, response time models, and network psychometrics in Chapter 6. The chapters start with the theory and methods of the measurement model and conclude with a real-data example illustrating the measurement model.
Table of Contents
Acknowledgments
Glossary of Notion and Acronyms
1. Measurement in the Social, Behavioral, and Health Sciences
Introduction
Methodological Procedures and Psychometric Measurement Models
Relation of Measurement Model Attribution Scale
Developing Attribute Theory is Important
Measurement Instruments
Measurement Models
Scales of Measurement
Causes of Messy Data
A Scale for Transitive Reasoning
Cycle of Instrument Construction
This Monograph
2. Classical Test Theory and Factor Analysis
Historical Introduction
The Classical Test Method
Measurement Level and Norm Scores
Model Assumptions
Repeatability of Test Scores: Reliability
Methods for Estimating Reliability
Methods Commonly Used in Test-Construction Practice
Parallel-test method
Retest Method
Split-Half Method
Internal Consistency Method
Reliability Methods Based on One Test Administration
Method
Method
Method
Method
Method
Method
Greatest Lower Bound
Special Topics Concerning Methods through and the GLB
Mutual Relationships of Lower Bounds and Reliability
Discrepancy of Methods through and the GLB
Overestimation of Reliability in Real Data
Confidence intervals
Reliability versus Measurement Precision
Traditional Methods
Alternative Methods and Special Topics
Constructing Scales in the Classical Test Theory Context
Corrected Item-Total Correlations and Oblique Multiple Group Method
Principal Component Analysis
Factor Analysis
Factor-analysis approach to reliability
One-Factor Model
Multi-Factor Model
Real-Data Example: The Type D Scale14 (DS14)
Discussion
3. Nonparametric Item Response Theory and Mokken Scale Analysis
Introduction
Model of Monotone Homogeneity
Prerequisites
Definitions and Notation
Assumptions
Strict and Essential Unidimensional IRT
An Ordinal Scale for Person Measurement
Goodness of Fit Methods
Unidimensionality: Scalability and Item Selection
Scalability Coefficients and Scale Definition
Modified Scalability Bounds
Mokken’s Automated Item Selection Procedure
Modified Procedure to Produce Maximum-Length Scales
Sample Size and Concluding Remarks
Monotonicity
Binning
Order-Restricted Likelihood Ratio Test
Kernel Smoothing
Polytomous-Item Monotonicity
Local Independence
The CA Method
The DETECT Method
Comparative Research
Data Example: The Type D Scale14 (DS14) Revisited Using Nonparametric IRT
Model of Double Monotonicity
Goodness of Fit Methods
Method Manifest Invariant Item Ordering
Other Methods for Investigating an Invariant Item Ordering
Reliability
Data Example: The Type D Scale14 (DS14) Continued
Discussion
4. Parametric Item Response Theory and Structural Extensions
Introduction
A Taxonomy for IRT Models
Some Basic IRT Models for Dichotomous Items
Guttman Model
Normal-Ogive Models
1-Parameter Logistic Model or Rasch Model
The Model, Separability of Parameters
Sufficiency and Estimation
Information Functions and Measurement Precision
Goodness of Fit Methods
The Rasch Paradox
Epilogue
2 and 3-Parameter Logistic Models
Some Basic IRT Models for Polytomous Items
Adjacent Category Models
Cumulative Probability Models
Continuation Ratio Models
Filling in the Taxonomy
IRT Models for Special Purposes
Linear Logistic Model
Generalized Rasch Model with Manifest Predictors
Multidimensional IRT Models
Data Example: Transitive Reasoning
Discussion
5. Latent Class Models and Cognitive Diagnostic Models
Introduction
Latent Class Model
An Example: Proportional Reasoning by means of the Balance Scale
Introduction
The Unrestricted Model
Restricted Models
Estimation
Goodness of Fit Methods
Likelihood Statistic
Assessing Individual Items
Information Fit Measures
Special Topics
Ordered LCM and Testing Monotonicity in Nonparametric IRT
Data Example: Proportional Reasoning by means of the Balance Scale
Discussion
Cognitive Diagnostic Model
An example: Identifying Patients’ Disorder Profiles Using the MCMI-III
Introduction
Models
Deterministic Input, Noisy "AND" Gate Model
Reduced Reparametrized Unified Model
Deterministic Input, Noisy "OR" Gate Model
General Diagnostic Model
Generalized-DINA or G-DINA Model
Log-Linear Cognitive Diagnostic Model
Estimation
Goodness of Fit Methods
Absolute Fit Assessment
Relative Fit Assessment
Relationship to Nonparametric IRT
Data Example: Identifying Patients’ Disorder Profiles Using the MCMI-III
Discussion
General Discussion
6. Pairwise Comparison, Proximity, Response Time, and Network Models
Introduction
Pairwise Comparison Models
Thurstone Model
Bradley-Terry-Luce Model
Discussion
Proximity Models
Deterministic Model
Probabilistic Models
Discussion
Response Time Models
Lognormal Model
Diffusion Model
Discussion
Network Psychometrics
Network Approach for Gaussian Data
Prerequisites for Gaussian Data Networks
Networks for Gaussian Data
Network Approach for Binary Data
Discussion
References
Biography
Klaas Sijtsma is a professor of Methods of Psychological Research at the Tilburg School of Social and Behavioral Sciences, Tilburg University, the Netherlands. His research specializes in psychometrics, in particular, all issues related to the measurement of psychological attributes by means of tests and questionnaires. He is a past President of the Psychometric Society, editorial board member for several journals, and has authored two other books on measurement.
Andries L. van der Ark is professor of Psychometrics at the Research Institute of Child Development and Education, Faculty of Social and Behavioural Sciences, University of Amsterdam, the Netherlands. His primary research interests include reliability analysis, nonparametric item response theory, and categorical data analysis. The authors have published over 40 papers together on measurement in the social and behavioral sciences.
"There are very few measurement textbooks that are accompanied with such a strong quantitative foundation, and those that are tend to be quite dated. This book is thus unique in providing a contemporary measurement text that is also designed for students that have a good quantitative background (as might be provided by a good introductory statistics course). Another very appealing feature of this book is its extensive coverage of various models and methodological tools that can be applied in the context of measurement. Network models and diagnostic models, for example, are relatively recent innovations in measurement. Having a single book covering all these techniques gives readers an appreciation for the different ways in which measurement can be considered from a quantitative perspective. The book would thus be an excellent choice for a graduate-level or advanced undergraduate-level measurement course. But the book would also function well as a reference text given the variety of topics covered." ~Daniel Bolt, University of Wisconsin, Madison
“I read the chapters with great interest. I think that a book like this is certainly useful as similar books are either too technical, too conceptual, or too narrow focused. In the chapters I read, the authors found a nice balance between technical and conceptual detail. This makes the book useful as both a textbook to be used for master students and as a reference book for (applied) researchers. I especially liked the boxes with derivations.”
~Dylan Molenaar, University of Amsterdam“I think many people could find this book useful. You could think of researchers in the social and behavorial sciences, Phd students, research master students and peer psychometricians. The additional value of this book is that it goes just beyond the basics of psychometrics. People may both use it as a reference and a textbook.”
~Samantha Bouwmeester, Erasmus University Rotterdam“It was a joy to read chapter 4. It was well written and interesting to persons who start with IRT and persons who worked with it for years. It explains the principles very well, as well has an eye for interesting subtleties.”
~Bas Hemker, CITO"This chapter 3 would be useful for statisticians, epidemiologists, psychometricians, methodologists, and mathematical psychologists who are working with social scientists or behavioral scientists, or in health care research or in educational research. It would also be useful for graduate students in the fields of statistics, epidemiology, etc. I would say that knowledge of statistics at an intermediate level is required."
~J.L. Ellis, Behavioural Science Institute, Radboud University"[This] is a comprehensive book summarizing a wide range of psychometric concepts and theories. Unlike introductory texts on psychological measurement, this book aims to get readers acquainted with statistical models and assumptions underlying psychometric theories. (...). Overall, this is a well-organized book that provides comprehensive coverage of both traditional and modern psychometric theories. The authors, who are well-known researchers in psychomet rics, provide valuable insights into psychometric theories and models through this book. For researchers, practitioners, and graduate students who want to build a solid foundation in psychometrics, this book would be a great resource to understand the relationships among various psychometric theories. Furthermore, readers with some knowledge of psychometrics may also benefit from this book to learn more about the advantages and disadvantages of different psychometric models."
~Hatice Cigdem Bulut, Okan Bulut, in Psychometrika, June 2021"The book is written for graduate and Ph.D. students, psychometricians and researchers in the areas of the social, behavioral, and health sciences. It can enrich other applied studies by new ideas and statistical techniques as well."
~Stan Lipovetsky, in Technometrics, July 2022