Computational Aspects of Psychometric Methods With R

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
Notation
Acronyms
Author bios
1. Introduction
	1.1. Brief history of psychometrics
	1.2. Measurement in social sciences
		1.2.1. Educational measurement
		1.2.2. Psychological assessment
		1.2.3. Health-related outcome measures
		1.2.4. Other areas of measurement
	1.3. Measurement data in this book
	1.4. Psychometrics with R
	1.5. Exploring measurement data
		1.5.1. Item scores
		1.5.2. Test scores
		1.5.3. Covariates and more complex data structures
	1.6. Modeling measurement data
	1.7. ShinyItemAnalysis interactive application
	1.8. Summary
2. Validity
	2.1. Introduction
	2.2. Sources of validity-supporting evidence
		2.2.1. Evidence based on test content
		2.2.2. Evidence based on relations to other variables
		2.2.3. Evidence based on internal structure
	2.3. Statistical methods in test validation
		2.3.1. Inferences based on ratios
		2.3.2. One sample and a paired t test
		2.3.3. Two sample t test
		2.3.4. More samples - ANOVA
		2.3.5. Correlation coefficients
		2.3.6. Regression models
			2.3.6.1. Simple linear regression
			2.3.6.2. Multiple regression
			2.3.6.3. More complex designs
	2.4. Further issues
		2.4.1. Estimation of model parameters
			2.4.1.1. Ordinary least squares method
			2.4.1.2. Maximum likelihood method
		2.4.2. Model selection and model fit
		2.4.3. Correction for range restriction
	2.5. Validity in interactive application
	2.6. Summary
3. Internal structure of the test and factor analysis
	3.1. Introduction
	3.2. Correlation structure
	3.3. Cluster analysis
	3.4. Factor analysis
		3.4.1. Exploratory factor analysis
			3.4.1.1. The single factor model
			3.4.1.2. More factors
		3.4.2. Factor rotation
		3.4.3. Factor scores
		3.4.4. The number of factors
		3.4.5. Model selection and model fit
		3.4.6. Confirmatory factor analysis
		3.4.7. Hierarchical and more complex structures
	3.5. Internal structure and FA in interactive application
	3.6. Summary
4. Reliability
	4.1. Introduction
	4.2. Formal definition and properties in CTT
		4.2.1. Definition of reliability
		4.2.2. Reliability as correlation between measurements
		4.2.3. Implications of low reliability
		4.2.4. Rules of thumb
		4.2.5. Reliability of composites
			4.2.5.1. Spearman-Brown prophecy formula
		4.2.6. Increasing reliability
	4.3. Estimation of reliability
		4.3.1. Reliability estimation with correlation coefficients
			4.3.1.1. Test-retest reliability
			4.3.1.2. Parallel forms
			4.3.1.3. Split-half coefficient
		4.3.2. Cronbach's alpha
			4.3.2.1. Cronbach's alpha and inter-item correlations
	4.4. Estimation of reliability with variance components
		4.4.1. ANOVA method of estimation
			4.4.1.1. One-way ANOVA
			4.4.1.2. Two-way ANOVA and Cronbach's alpha
		4.4.2. Maximum likelihood
		4.4.3. Restricted maximum likelihood
		4.4.4. Bootstrap confidence intervals
		4.4.5. Bayesian estimation
	4.5. More sources of error and G-theory
		4.5.1. A one-facet study
		4.5.2. A two-facet study
	4.6. Other estimates of reliability
	4.7. Reliability in interactive application
	4.8. Summary
5. Traditional item analysis
	5.1. Introduction
	5.2. Item difficulty
		5.2.1. Difficulty in binary items
		5.2.2. Difficulty in ordinal items
	5.3. Item discrimination
		5.3.1. Correlation between item and total score
		5.3.2. Difference between upper and lower group
	5.4. Item characteristic curve
	5.5. Distractor analysis
	5.6. Reliability if an item is dropped
	5.7. Item validity
	5.8. Missed items
	5.9. Item analysis in interactive application
	5.10. Summary
6. Item analysis with regression models
	6.1. Introduction
	6.2. Model specification
	6.3. Models for continuous items
		6.3.1. Linear regression model
	6.4. Models for binary items
		6.4.1. Logistic regression model
		6.4.2. Other link functions, probit regression model
		6.4.3. IRT parametrization
		6.4.4. Nonlinear regression models
	6.5. Estimation of item parameters
		6.5.1. Nonlinear least squares
		6.5.2. Maximum likelihood method
	6.6. Model selection
		6.6.1. Likelihood-ratio test
		6.6.2. Akaike information criterion
		6.6.3. Bayesian information criterion
	6.7. Models for polytomous items
		6.7.1. Ordinal regression models
			6.7.1.1. Cumulative logit model
			6.7.1.2. Adjacent-categories logit model
		6.7.2. Multinomial regression models
	6.8. Joint model
		6.8.1. Person-item map
	6.9. Regression models in interactive application
	6.10. Summary
7. Item response theory models
	7.1. Introduction
	7.2. General concepts and assumptions
		7.2.1. IRT model assumptions
		7.2.2. IRT models for binary data
			7.2.2.1. Rasch or 1PL IRT model
			7.2.2.2. 2PL IRT model
			7.2.2.3. Normal-ogive model
			7.2.2.4. 3PL IRT model
			7.2.2.5. 4PL IRT model
	7.3. Estimation methods for IRT models
		7.3.1. Heuristic methods and starting values
		7.3.2. Joint maximum likelihood
		7.3.3. Conditional maximum likelihood
		7.3.4. Marginal maximum likelihood
			7.3.4.1. Estimation of person abilities in MML
		7.3.5. Bayesian IRT models
		7.3.6. Item and test information
		7.3.7. Model selection and model fit
	7.4. Binary IRT models in R
		7.4.1. The mirt package
		7.4.2. The ltm package
		7.4.3. The eRm package
		7.4.4. Other IRT packages
			7.4.4.1. The TAM package
			7.4.4.2. The ShinyItemAnalysis package
		7.4.5. The lme4 and nlme packages
		7.4.6. Bayesian IRT with the brms package
	7.5. Relationship between IRT and factor analysis
	7.6. IRT models in interactive application
	7.7. Summary
8. More complex IRT models
	8.1. Introduction
	8.2. IRT models for polytomous items
		8.2.1. Cumulative logit IRT models
			8.2.1.1. Graded response model
			8.2.1.2. Graded rating scale model
		8.2.2. Adjacent-categories logit IRT models
			8.2.2.1. Generalized partial credit model
			8.2.2.2. Partial credit model
			8.2.2.3. Rating scale model
		8.2.3. Baseline-category logit IRT models
			8.2.3.1. Nominal response model
		8.2.4. Other IRT models for polytomous data
		8.2.5. Item-specific IRT models
	8.3. Multidimensional IRT models
		8.3.1. Multidimensional 2PL model
		8.3.2. Multidimensional graded response model
		8.3.3. Confirmatory multidimensional IRT models
	8.4. Estimation in more complex IRT models
		8.4.1. Maximum likelihood methods
		8.4.2. Regularization methods
		8.4.3. Bayesian methods with MCMC and MH-RM
		8.4.4. Model selection and model fit
	8.5. More complex IRT models in interactive application
	8.6. Summary
9. Differential item functioning
	9.1. Introduction
	9.2. Definition
		9.2.1. DIF examples and interpretations
		9.2.2. Matching criterion
	9.3. Traditional DIF detection methods
		9.3.1. Delta plot method
		9.3.2. Mantel-Haenszel test
		9.3.3. SIBTEST
	9.4. DIF detection based on regression models
		9.4.1. Logistic regression
			9.4.1.1. Testing for DIF
		9.4.2. Generalized logistic regression models
		9.4.3. Group-specific cumulative logit model
		9.4.4. Group-specific adjacent category logit model
		9.4.5. Group-specific multinomial regression model
	9.5. IRT-based DIF detection methods
		9.5.1. Group-specific IRT models
		9.5.2. Lord's test
		9.5.3. Likelihood-ratio test
		9.5.4. Raju's test
	9.6. Other methods
		9.6.1. Iterative hybrid ordinal logistic regression with IRT
		9.6.2. Regularization approach for DIF detection
		9.6.3. Measurement invariance: Factor analytic approach
	9.7. DIF detection in interactive application
	9.8. Summary
10. Outlook on applications and more advanced psychometric topics
	10.1. Introduction
	10.2. Computerized adaptive testing
		10.2.1. Item bank
		10.2.2. Ability estimation
		10.2.3. Item selection algorithms
		10.2.4. Stopping rules
		10.2.5. CAT implementation in interactive application
		10.2.6. Post-hoc analysis
		10.2.7. CAT simulation study with MCMC
	10.3. Test equating and linking
	10.4. Generalizing latent variable models
	10.5. Big data and computational psychometrics
	10.6. Interactive psychometric modules
	10.7. Summary
A: Introduction to R
	A.1. Obtaining and running R and RStudio
	A.2. Starting with R
	A.3. Installation of R packages
	A.4. Data handling in R
		A.4.1. Data types in R
		A.4.2. Wide and long data format
		A.4.3. Data handling with tidyverse
	A.5. Graphics in R
		A.5.1. Graphics in base R
		A.5.2. Graphics with the ggplot2 package
		A.5.3. Trellis graphics with the lattice package
	A.6. Interactive Shiny applications
B: Descriptive statistics
C: Distributions of random variables
	C.1. Discrete random variables
	C.2. Continuous random variables
D: Measurement data in ShinyItemAnalysis
E: Exercises
	E.1. Exercises for Chapter 1
	E.2. Exercises for Chapter 2
	E.3. Exercises for Chapter 3
	E.4. Exercises for Chapter 4
	E.5. Exercises for Chapter 5
	E.6. Exercises for Chapter 6
	E.7. Exercises for Chapter 7
	E.8. Exercises for Chapter 8
	E.9. Exercises for Chapter 9
	E.10. Exercises for Chapter 10
References
Index