*A Course in Item Response Theory and Modeling with Stata,* by Tenko Raykov and George A. Marcoulides, is a comprehensive introduction to the concepts of item response theory (IRT) that includes numerous examples using Stata’s powerful suite of IRT commands. The authors’ unique development of IRT builds on the foundations of classical test theory, nonlinear factor analysis, and generalized linear models. The examples demonstrate how to fit many kinds of IRT models, including one-, two-, and three-parameter logistic models for binary items as well as nominal, ordinal, and hybrid models for polytomous items.

Chapters 1 and 2 define item response theory and review the statistical concepts and functions that are used to build item response models.

Chapters 3 and 4 discuss classical test theory, factor analysis, and generalized linear models, which provide the conceptual foundations of item response theory.

Chapters 5 and 6 introduce the fundamentals of item response theory and provide examples to illustrate the concepts.

Chapters 7 and 8 cover model fitting, estimation using maximum likelihood theory, item characteristic curves, and information functions.

Chapters 9 and 10 provide a detailed introduction to instrument construction and differential item functioning.

Chapters 11 and 12 introduce IRT models for nominal and ordinal responses as well as multidimentional IRT models.

*A Course in Item Response Theory and Modeling with Stata* is an outstanding text both for those who are new to IRT and for those who are familiar with IRT but new to fitting these models in Stata. It is a useful text for IRT courses and for researchers who use IRT.

© Copyright 1996–2023 StataCorp LLC

**List of figures**

**List of tables**

**Preface**

**Notation and typography**

1.2 The factor analysis connection

1.3 What this book is, and is not, about

1.4 Chapter conclusion

2.1 The normal ogive

2.1.2 The normal ogive function

2.2 The logistic function and related concepts

2.2.2 Invertibility of the logistic function, odds, and logits

2.3 The relationship between the logistic and normal ogive functions and their use to express response probability

2.3.2 Alternative response probability as closely related to the logistic function

2.4 Chapter conclusion

3.1 A brief visit to classical test theory

3.1.2 Misconceptions about classical test theory

3.1.3 Binary random variables: Expectation and probability of a prespecified response

3.2 Why classical test theory?

3.3 A short introduction to classical factor analysis

3.3.2 Model parameters

3.3.3 Classical factor analysis and measure correlation for fixed factor values

3.4 Chapter conclusion

4.1 Generalized linear modeling as a statistical methodology for analysis of relationships between response and explanatory variables

4.1.2 Extending the linear modeling idea to discrete response variables

4.1.3 The components of a generalized linear model

4.2 Logistic regression as a generalized linear model of relevance for item response theory and item response modeling

4.2.2 Multivariate logistic regression

4.3 Nonlinear factor analysis models and their relation to generalized linear models

4.3.2 Nonlinear factor analysis models

4.4 Chapter conclusion

5.1 Item characteristic curves revisited

5.2 Unidimensionality and local independence

5.2.2 A formal definition of local independence

5.2.3 What does it mean to assume local independence in an item response theory setting?

5.3 A general linear modeling property yielding test-free and group-free measurement in item response modeling

5.4 One more look at the logistic function

5.5 The one- and two-parameter logistic models

5.5.2 Interpretation of the item parameters in the two-parameter logistic model

5.5.3 The scale of measurement

5.5.4 The one-parameter logistic model

5.5.5 The one-parameter logistic and two-parameter logistic models as nonlinear factor analysis models, generalized linear models, and logistic regression models

5.5.6 Important and useful properties of the Rasch model

5.6 The three-parameter logistic model

5.7 The logistic models as latent variable models and analogs to nonlinear regression models

5.7.2 The logistic models as analogs to nonlinear regression models

5.8 Chapter conclusion

6.2 Fitting a two-parameter logistic model

6.3 Testing nested item response theory models and model selection

6.4 Fitting a one-parameter logistic model and comparison with the two-parameter logistic model

6.5 Fitting a three-parameter logistic model and comparison with more parsimonious models

6.6 Estimation of individual subject trait, construct, or ability levels

6.7 Scoring of studied persons

6.8 Chapter conclusion

7.2 Person likelihood function for a given item set

7.2.2 Maximum likelihood estimation of trait or ability level for a given person

7.2.3 A brief visit to the general maximum likelihood theory

7.2.4 What if (meaningful) maximum likelihood estimates do not exist?

7.3 Estimation of item parameters

7.4 Estimation of item and ability parameters

7.5 Testing and selection of nested item response theory models

7.6 Item response model fitting and estimation with missing data

7.7 Chapter conclusion

8.2 Why should one be interested in item information, and where is it maximal?

8.3 What else is relevant for item information?

8.4 Empirical illustration of item information functions

8.5 Test information function

8.6 Test characteristic curve

8.7 The test characteristic curve as a nonlinear trait or ability score transformation

8.8 Chapter conclusion

9.2 How to apply Lord’s approach to instrument construction in empirical research

9.3 Examples of target information functions for applications of the outlined procedure for measuring instrument construction

9.4 Assumptions of instrument construction procedure

9.5 Discussion and conclusion

10.2 Two main approaches to differential item functioning examination

10.3 Observed variable methods for differential item functioning examination

10.4 Using Stata for studying differential item functioning with observed variable methods

10.5 Item response theory based methods for differential item functioning examination

10.6 Chapter conclusion

**Appendix. The Benjamin–Hochberg multiple testing procedure: A brief introduction**

11.2 A key distinction between item response theory models with polytomous and dichotomous items

11.3 The nominal response model

11.4 The partial credit and the rating scale models

11.4.2 Rating scale model

11.5 The generalized partial credit model

11.6 The graded response model

11.7 Comparison and selection of polytomous item response models

11.8 Hybrid models

11.9 The three-parameter logistic model revisited

11.10 Chapter conclusion

12.2 A main methodological principle underlying multidimensional item response theory

12.3 How can we define multidimensional item response theory?

12.4 A main class of multidimensional item response theory models

12.5 Fitting multidimensional item response theory models and comparison with unidimensional item response theory models

12.5.2 Comparing a multidimensional model with an unidimensional model

12.6 Chapter conclusion

**References**

**Author Index**

© Copyright 1996–2023 StataCorp LLC