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Contents
Preface
List of Figures
List of Tables
1 Introduction to the R Programming Language
1.1 Chapter Overview
1.2 What Is R?
1.2.1 Our Approach to R
1.3 Obtaining and Installing R
1.3.1 Windows
1.3.2 Mac
1.3.3 Linux
1.4 Obtaining and Installing RStudio
1.5 Using R
1.5.1 Basic R Usage
1.5.2 R Packages
1.5.2.1 Masked Functions
1.5.3 Assessing and Reading in Data
1.5.4 Data Manipulation
1.5.5 Descriptive and Inferential Statistics
1.5.6 Plotting in R
1.5.6.1 Base R Graphics
1.5.6.2 Lattice Graphics
1.6 Installing Packages Used in This Handbook
1.7 Chapter Summary
2 Classical Test Theory
2.1 Chapter Overview
2.2 What Is Measurement?
2.3 Issues in Measurement
2.3.1 Type of Scales
2.4 The Classical Test Theory Framework
2.4.1 Reliability
2.4.2 Validity
2.4.3 Item Analysis
2.5 Summary
3 Generalizability Theory
3.1 Chapter Overview
3.2 Introduction
3.3 Examples
3.3.1 One-Facet Design
3.3.1.1 G Study
3.3.1.2 D Study
3.3.2 Two-Facet Crossed Design
3.3.2.1 G Study
3.3.2.2 D Study
3.3.3 Two-Facet Partially Nested Design
3.3.3.1 G Study
3.3.3.2 D Study
3.3.4 Two-Facet Crossed Design with a Fixed Facet
3.3.4.1 G Study
3.3.4.2 D Study
3.4 Summary
4 Factor Analytic Approach in Measurement
4.1 Chapter Overview
4.2 Introduction
4.3 Exploratory Factor Analysis (EFA)
4.3.1 EFA of a Cognitive Inventory
4.3.2 EFA Using the psych Package
4.3.3 EFA with Categorical Data
4.4 Confirmatory Factor Analysis (CFA)
4.4.1 CFA of the WISC-R Data
4.4.2 CFA with Categorical Data
4.4.2.1 Ordinal CFA–Method 1
4.4.2.2 Ordinal CFA–Method 2
4.5 Summary
5 Item Response Theory for Dichotomous Items
5.1 Chapter Overview
5.2 Introduction
5.2.1 Comparison to Classical Test Theory
5.2.2 Basic Concepts in IRT
5.2.3 IRT Model Assumptions
5.3 The Unidimensional IRT Models for Dichotomous Items
5.3.1 One-Parameter Logistic Model and Rasch Model
5.3.1.1 One-Parameter Logistic Model
5.3.1.2 Rasch Model
5.3.2 Two-Parameter Logistic Model
5.3.3 Three-Parameter Logistic Model
5.3.4 Four-Parameter Logistic Model
5.4 Ability Estimation in IRT Models
5.5 Model Diagnostics
5.5.1 Item Fit
5.5.2 Person Fit
5.5.3 Model Selection
5.6 Summary
6 Item Response Theory for Polytomous Items
6.1 Chapter Overview
6.2 Polytomous Rasch Models for Ordinal Items
6.2.1 Partial Credit Model
6.2.2 Rating Scale Model
6.3 Polytomous Non-Rasch Models for Ordinal Items
6.3.1 Generalized Partial Credit Model
6.3.2 Graded Response Model
6.4 Polytomous IRT Models for Nominal Items
6.4.1 Nominal Response Model
6.4.2 Nested Logit Model
6.5 Model Selection
6.6 Summary
7 Multidimensional Item Response Theory
7.1 Chapter Overview
7.2 Multidimensional Item Response Modeling
7.2.1 Compensatory and Noncompensatory MIRT
7.2.2 Between-Item and Within-Item Multidimensionality
7.2.3 Exploratory and Confirmatory MIRT Analysis
7.3 Common MIRT Models
7.3.1 Multidimensional 2PL Model
7.3.2 Multidimensional Rasch Model
7.3.3 Multidimensional Graded Response Model
7.3.4 Bi-Factor IRT Model
7.4 Summary
8 Explanatory Item Response Theory
8.1 Chapter Overview
8.2 Explanatory Item Response Modeling
8.2.1 Data Structure
8.2.2 Rasch Model as a GLMM
8.2.3 Linear Logistic Test Model
8.2.4 Latent Regression Rasch Model
8.2.5 Interaction Models
8.3 Summary
9 Visualizing Data and Measurement Models
9.1 Chapter Overview
9.2 Introduction
9.3 Diagnostic Plots
9.4 Path Diagrams
9.5 Interactive Plots with shiny
9.5.1 Example 1: Diagnostic Plot for Factor Analysis
9.5.2 Example 2: The 3PL IRT Model
9.6 Summary
10 Equating
10.1 Overview
10.2 Introduction
10.2.1 Equating Designs
10.2.2 Equating Functions and Methods
10.2.3 Evaluating the Results
10.2.4 Further Reading
10.3 Examples
10.3.1 Equivalent Groups
10.3.1.1 Identity, Mean, and Linear Functions
10.3.1.2 Nonlinear Functions
10.3.2 Nonequivalent Groups
10.3.2.1 Linear Tucker Equating
10.4 Summary
11 Measurement Invariance and Differential Item Functioning
11.1 Chapter Overview
11.2 Measurement Invariance
11.2.1 Assessing Measurement Invariance
11.2.1.1 Configural Invariance
11.2.1.2 Weak Invariance
11.2.1.3 Strong Invariance
11.2.1.4 Strict Invariance
11.2.1.5 Assessing Partial Invariance
11.3 Differential Item Functioning
11.3.1 The Mantel-Haenszel (MH) Method
11.3.2 Logistic Regression
11.3.3 Item Response Theory Likelihood Ratio Test
11.4 Summary
12 More Advanced Topics in Measurement
12.1 Chapter Overview
12.2 CRAN Task Views
12.3 Computerized Adaptive Testing
12.4 Cognitive Diagnostic Modeling
12.5 IRT Linking Procedures
12.6 Bayesian Models of Measurement
12.7 Hierarchical Linear Models
12.8 Profile Analysis
12.9 Summary
References
Index
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1.1 Default RStudio setup after creating a new R script.
1.2 Default diagnostic plots from a multiple regression model.
1.3 Scatter plot matrix of verbal measures in the interest data set.
1.4 Scatter plot of vocab by reading conditional on gender.
2.1 Dot plot of age by sex of examinees taking the interest inventory.
2.2 Q–Q plot of the vocab variable in the interest data set.
2.3 Empirical distribution for coefficient alpha (n = 10,000).
3.1 Venn diag...
