1st Edition

Measurement Models for Psychological Attributes

    428 Pages 50 B/W Illustrations
    by Chapman & Hall

    428 Pages 50 B/W Illustrations
    by Chapman & Hall

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    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


    Glossary of Notion and Acronyms

    1. Measurement in the Social, Behavioral, and Health Sciences


    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







    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)


    3. Nonparametric Item Response Theory and Mokken Scale Analysis


    Model of Monotone Homogeneity


    Definitions and Notation


    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



    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


    Data Example: The Type D Scale14 (DS14) Continued


    4. Parametric Item Response Theory and Structural Extensions


    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


    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


    5. Latent Class Models and Cognitive Diagnostic Models


    Latent Class Model

    An Example: Proportional Reasoning by means of the Balance Scale


    The Unrestricted Model

    Restricted Models


    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


    Cognitive Diagnostic Model

    An example: Identifying Patients’ Disorder Profiles Using the MCMI-III



    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


    Goodness of Fit Methods

    Absolute Fit Assessment

    Relative Fit Assessment

    Relationship to Nonparametric IRT

    Data Example: Identifying Patients’ Disorder Profiles Using the MCMI-III


    General Discussion

    6. Pairwise Comparison, Proximity, Response Time, and Network Models


    Pairwise Comparison Models

    Thurstone Model

    Bradley-Terry-Luce Model


    Proximity Models

    Deterministic Model

    Probabilistic Models


    Response Time Models

    Lognormal Model

    Diffusion Model


    Network Psychometrics

    Network Approach for Gaussian Data

    Prerequisites for Gaussian Data Networks

    Networks for Gaussian Data

    Network Approach for Binary Data




    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