Measurement Models for Psychological Attributes  book cover
1st Edition

Measurement Models for Psychological Attributes

ISBN 9780367424527
Published October 23, 2020 by Chapman and Hall/CRC
428 Pages 50 B/W Illustrations

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Book Description

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

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



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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