Handbook of educational measurement and psychometrics using R

327 Pages·2018·34.456 MB·English

by  Bulut, Okan, Desjardins, Christopher David

Handbook of
Educational
Measurement
and Psychometrics
Using R
Chapman & Hall/CRC
The R Series
Series Editors
John M. Chambers Torsten Hothorn
Department of Statistics Division of Biostatistics
Stanford University University of Zurich
Stanford, California, USA Switzerland
Duncan Temple Lang Hadley Wickham
Department of Statistics RStudio
University of California, Davis Boston, Massachusetts, USA
Davis, California, USA
Basics of Matrix Algebra for Statistics with R
Nick Fieller
Introductory Fisheries Analyses with R
Derek H. Ogle
Statistics in Toxicology Using R
Ludwig A. Hothorn
Spatial Microsimulation with R
Robin Lovelace, Morgane Dumont
Extending R
John M. Chambers
Using the R Commander: A Point-and-Click Interface for R
John Fox
Computational Actuarial Science with R
Arthur Charpentier
bookdown: Authoring Books and Technical Documents with R Markdown
Yihui Xie
Testing R Code
Richard Cotton
R Primer, Second Edition
Claus Thorn Ekstrøm
Flexible Regression and Smoothing: Using GAMLSS in R
Mikis D. Stasinopoulos, Robert A. Rigby, Gillian Z. Heller, Vlasios Voudouris,
and Fernanda De Bastiani
The Essentials of Data Science: Knowledge Discovery Using R
Graham J. Williams
blogdown: Creating Websites with R Markdown
Yihui Xie, Alison Presmanes Hill, and Amber Thomas
For more information about this series, please visit: https://www.crcpress.
com/go/the-r-series
Handbook of
Educational
Measurement
and Psychometrics
Using R
Christopher D. Desjardins
Okan Bulut
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
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Version Date: 20180403
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Library of Congress Cataloging-in-Publication Data
Names: Desjardins, Christopher David, author. | Bulut, Okan, author.
Title: Handbook of educational measurement and psychometrics using R : By
Christopher David Desjardins, Okan Bulut.
Description: Boca Raton, Florida : CRC Press, [2018] | Includes
bibliographical references and index.
Identifiers: LCCN 2017057935| ISBN 9781498770132 (hardback : alk. paper) |
ISBN 9781315154268 (e-book : alk. paper) | ISBN 9781498770149 (e-book
(pdf) : alk. paper) | ISBN 9781351650304 (e-book (epub) : alk. paper) |
ISBN 9781351640770 (e-book (mobi/kindle) : alk. paper)
Subjects: LCSH: Educational tests and measurements--Handbooks, manuals, etc.
| Psychometrics--Methodology--Handbooks, manuals, etc. | R (Computer
program language)--Handbooks, manuals, etc.
Classification: LCC LB3051 .D4465 2018 | DDC 371.26--dc23
LC record available at https://lccn.loc.gov/2017057935
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
http://www.crcpress.com
CDD: To Kirsten
OB: To my parents and my brother

Contents
Preface xiii
List of Figures xix
List of Tables xxiii
1 Introduction to the R Programming Language 1
1.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 What Is R? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Our Approach to R . . . . . . . . . . . . . . . . . . . 2
1.3 Obtaining and Installing R . . . . . . . . . . . . . . . . . . . 3
1.3.1 Windows . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Mac . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.3 Linux . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Obtaining and Installing RStudio . . . . . . . . . . . . . . . 4
1.5 Using R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5.1 Basic R Usage . . . . . . . . . . . . . . . . . . . . . . 7
1.5.2 R Packages . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5.2.1 Masked Functions . . . . . . . . . . . . . . . 13
1.5.3 Assessing and Reading in Data . . . . . . . . . . . . . 14
1.5.4 Data Manipulation . . . . . . . . . . . . . . . . . . . . 16
1.5.5 Descriptive and Inferential Statistics . . . . . . . . . . 21
1.5.6 Plotting in R . . . . . . . . . . . . . . . . . . . . . . . 25
1.5.6.1 Base R Graphics . . . . . . . . . . . . . . . . 25
1.5.6.2 Lattice Graphics . . . . . . . . . . . . . . . . 27
1.6 Installing Packages Used in This Handbook . . . . . . . . . . 28
1.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Classical Test Theory 31
2.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2 What Is Measurement? . . . . . . . . . . . . . . . . . . . . . 31
2.3 Issues in Measurement . . . . . . . . . . . . . . . . . . . . . 32
2.3.1 Type of Scales . . . . . . . . . . . . . . . . . . . . . . 33
2.4 The Classical Test Theory Framework . . . . . . . . . . . . . 40
2.4.1 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4.2 Validity . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.3 Item Analysis . . . . . . . . . . . . . . . . . . . . . . . 49
vii
viii Contents
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 Generalizability Theory 55
3.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.1 One-Facet Design. . . . . . . . . . . . . . . . . . . . . 60
3.3.1.1 G Study . . . . . . . . . . . . . . . . . . . . 60
3.3.1.2 D Study . . . . . . . . . . . . . . . . . . . . 64
3.3.2 Two-Facet Crossed Design . . . . . . . . . . . . . . . . 66
3.3.2.1 G Study . . . . . . . . . . . . . . . . . . . . 66
3.3.2.2 D Study . . . . . . . . . . . . . . . . . . . . 68
3.3.3 Two-Facet Partially Nested Design . . . . . . . . . . . 69
3.3.3.1 G Study . . . . . . . . . . . . . . . . . . . . 70
3.3.3.2 D Study . . . . . . . . . . . . . . . . . . . . 71
3.3.4 Two-Facet Crossed Design with a Fixed Facet . . . . . 72
3.3.4.1 G Study . . . . . . . . . . . . . . . . . . . . 72
3.3.4.2 D Study . . . . . . . . . . . . . . . . . . . . 73
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 Factor Analytic Approach in Measurement 75
4.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3 Exploratory Factor Analysis (EFA) . . . . . . . . . . . . . . 76
4.3.1 EFA of a Cognitive Inventory . . . . . . . . . . . . . . 77
4.3.2 EFA Using the psych Package . . . . . . . . . . . . . 89
4.3.3 EFA with Categorical Data . . . . . . . . . . . . . . . 91
4.4 Confirmatory Factor Analysis (CFA) . . . . . . . . . . . . . 93
4.4.1 CFA of the WISC-R Data . . . . . . . . . . . . . . . . 93
4.4.2 CFA with Categorical Data . . . . . . . . . . . . . . . 103
4.4.2.1 Ordinal CFA–Method 1 . . . . . . . . . . . . 103
4.4.2.2 Ordinal CFA–Method 2 . . . . . . . . . . . . 105
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5 Item Response Theory for Dichotomous Items 107
5.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1 Comparison to Classical Test Theory . . . . . . . . . . 107
5.2.2 Basic Concepts in IRT . . . . . . . . . . . . . . . . . . 108
5.2.3 IRT Model Assumptions . . . . . . . . . . . . . . . . . 112
5.3 The Unidimensional IRT Models for Dichotomous Items . . . 113
5.3.1 One-Parameter Logistic Model and Rasch Model . . . 113
5.3.1.1 One-Parameter Logistic Model . . . . . . . . 113
5.3.1.2 Rasch Model . . . . . . . . . . . . . . . . . . 119
5.3.2 Two-Parameter Logistic Model . . . . . . . . . . . . . 122
Contents ix
5.3.3 Three-Parameter Logistic Model . . . . . . . . . . . . 124
5.3.4 Four-Parameter Logistic Model . . . . . . . . . . . . . 126
5.4 Ability Estimation in IRT Models . . . . . . . . . . . . . . . 128
5.5 Model Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . 133
5.5.1 Item Fit . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.5.2 Person Fit . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.5.3 Model Selection . . . . . . . . . . . . . . . . . . . . . . 139
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6 Item Response Theory for Polytomous Items 143
6.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 143
6.2 Polytomous Rasch Models for Ordinal Items . . . . . . . . . 144
6.2.1 Partial Credit Model . . . . . . . . . . . . . . . . . . . 144
6.2.2 Rating Scale Model . . . . . . . . . . . . . . . . . . . 148
6.3 Polytomous Non-Rasch Models for Ordinal Items . . . . . . 151
6.3.1 Generalized Partial Credit Model . . . . . . . . . . . . 152
6.3.2 Graded Response Model . . . . . . . . . . . . . . . . . 154
6.4 Polytomous IRT Models for Nominal Items . . . . . . . . . . 157
6.4.1 Nominal Response Model . . . . . . . . . . . . . . . . 158
6.4.2 Nested Logit Model . . . . . . . . . . . . . . . . . . . 161
6.5 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7 Multidimensional Item Response Theory 169
7.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 169
7.2 Multidimensional Item Response Modeling . . . . . . . . . . 170
7.2.1 Compensatory and Noncompensatory MIRT . . . . . 170
7.2.2 Between-Item and Within-Item Multidimensionality . 172
7.2.3 Exploratory and Confirmatory MIRT Analysis . . . . 174
7.3 Common MIRT Models . . . . . . . . . . . . . . . . . . . . . 175
7.3.1 Multidimensional 2PL Model . . . . . . . . . . . . . . 175
7.3.2 Multidimensional Rasch Model . . . . . . . . . . . . . 184
7.3.3 Multidimensional Graded Response Model . . . . . . . 187
7.3.4 Bi-Factor IRT Model . . . . . . . . . . . . . . . . . . . 189
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8 Explanatory Item Response Theory 193
8.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2 Explanatory Item Response Modeling . . . . . . . . . . . . . 193
8.2.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . 194
8.2.2 Rasch Model as a GLMM . . . . . . . . . . . . . . . . 196
8.2.3 Linear Logistic Test Model . . . . . . . . . . . . . . . 199
8.2.4 Latent Regression Rasch Model . . . . . . . . . . . . . 203
8.2.5 Interaction Models . . . . . . . . . . . . . . . . . . . . 206
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210