The first edition of Item Response Theory for Psychologists by Susan Embretson and Steven Reise (Reference Embretson and Reise2000) has been the book I most frequently recommend to students and applied researchers seeking an accessible introduction to item response theory (IRT). Now retitled Item Response Theory: Foundations for Psychologists and Social Scientists, the second edition comes 25 years later with an updated and larger scope. While the book has many strengths that set it apart from other introductory texts, including its more applied focus and heavy use of real data examples, it is the emphasis on the psychology behind the psychometrics that I find most valuable. Throughout the book, modeling decisions are motivated by substantive psychological questions and theories, particularly those concerning construct validity. The goal is to better understand the construct, not simply optimize model fit. This perspective reflects both authors’ broader contributions to the field, which bridge methodology and psychology: Embretson’s work on explanatory IRT and cognitive models (e.g., Embretson, Reference Embretson1998; Whitely, Reference Whitely1980), and Reise’s work on bifactor models (e.g., Reise, Reference Reise2012) and the measurement of psychopathology (e.g., Reise et al., Reference Reise, Du, Wong, Hubbard and Haviland2021; Reise & Rodriguez, Reference Reise and Rodriguez2016; Reise & Waller, Reference Reise and Waller2009).

Item response theory has evolved considerably since the publication of the first edition in 2000, with developments in areas such as multidimensional and explanatory IRT, response time modeling, and software implementation. In this new edition, nearly every chapter has been revised to incorporate the most important advances from the last two decades. Some revisions are minor and involve changes to the organization or presentation of the material, whereas others are more substantial, including new chapters on software implementation, multidimensional IRT, and advanced models that incorporate covariates or response times. The book is geared toward graduate students and applied social science researchers who have familiarity with linear regression and basic probability. It is probably most accessible to readers who have also had some exposure to factor analysis or measurement theory, though it does not assume prior coursework in IRT. The book is organized into five sections: Introduction, Basic Item Response Theory Models, Estimating Item Parameters and Scoring Persons, Applications of Item Response Theory Models in Test Development and Assessment, and Advanced IRT Models. I have organized my review around these five sections, focusing primarily on what is new or substantially expanded.

The first three chapters comprise the Introduction (Section I), describing the background and history of IRT (Chapter 1) and comparing model-based measurement with the classical test theory (CTT) framework, emphasizing the many advantages of IRT (Chapters 2 and 3). Importantly, IRT is no longer just presented as an alternative to classical test theory; it is presented as the state-of-the-art framework for scale development and analysis. As Embretson and Reise state themselves, the goal of these chapters is to help students develop an intuitive understanding of foundational IRT concepts and model-based measurement. Part of what makes this book so accessible to non-methodologists is the way the authors connect new concepts to familiar ideas. They often start with an analogy and then follow up with a more thorough and technical treatment of the concept. For example, they compare latent trait estimation to clinical diagnosis, where an underlying disorder is not directly observed but must be inferred from observable symptoms. Similarly, IRT uses observed item responses to make inferences about the underlying latent trait.

Section II includes two chapters covering IRT models for binary (Chapter 4) and polytomous (Chapter 5) responses. The chapter on binary models presents the Rasch, 1PL, 2PL, and 3PL models and discusses the differences between the Rasch and non-Rasch modeling traditions. The chapter on polytomous models has been expanded considerably from the first edition, drawing attention to the many more modern applications of IRT to personality, psychopathology, and patient-reported outcomes. The models are organized according to the response processes they are intended to represent, helping readers understand both the similarities and differences among them. The authors use data visualizations to convey the most important concepts (e.g., category, threshold, and item response curves) and provide careful interpretations of all model parameters. I especially appreciated their discussion of the nominal response model (NRM) as the most general model and thoughtful explanation of how its category slope parameters inform response category ordering (a characteristic of the NRM that can be counterintuitive even for experienced users of IRT). Embretson and Reise are clear about the limitations of fit statistics in model selection. They recommend that researchers keep the proposed underlying response process in mind when deciding among different models. Outputs such as test information and trait estimates should be compared across candidate models, and researchers should consider interpretability and parsimony in addition to fit statistics. Both chapters provide an important foundation for the more advanced material that follows.

Section III is about measuring persons, estimating model parameters, and evaluating model assumptions and fit. The authors strike an appropriate balance in their chapters on measuring persons (Chapter 6) and item parameter estimation (Chapter 7), keeping only the most important technical details in the main text while moving more advanced derivations to an appendix. This judgment about what to include and what to leave out is one of the book’s strengths. Readers are provided enough information to understand the most important concepts without being bogged down by detail that is not critical for model application. Chapter 6 covers maximum likelihood (ML), maximum a posteriori (MAP), and expected a posteriori (EAP) scoring and includes a useful section explaining how latent trait scores can be viewed as weighted summed scores with weights derived from the IRT model. The chapter on estimating item parameters (Chapter 7) is unsurprisingly one of the denser chapters of the book. It begins with item factor analysis as a tool for assessing dimensionality and local independence. The authors then use simple heuristic examples to help readers develop an intuition for estimation before turning to the traditional maximum likelihood approaches for estimating the parameters of standard IRT models: marginal (MML), conditional (CML), and joint (JML) maximum likelihood. While most of the chapter remains in the frequentist framework, the authors also provide a limited overview of Bayesian approaches, noting that these methods are typically reserved for models more complex than those covered in this book. They also briefly mention more specialized estimation algorithms, such as Metropolis–Hastings Robbins–Monro (MH-RM), for high-dimensional models. Estimation is a challenging topic for most students, but the authors do a nice job of explaining the logic of different estimators without excessive mathematics. I found the description of the Newton–Raphson algorithm especially easy to follow for a topic that is often presented in a highly technical way.

The chapter on testing assumptions and assessing fit (Chapter 8) is my favorite chapter of the book; it walks the reader through several methods of model evaluation while emphasizing that model evaluation is as much an art as it is a science. The chapter opens with a quote from Embretson that nicely summarizes the theme of the chapter: “There are many things to do, but no one really knows what to do.” Rather than offering universal benchmarks for “acceptable” fit, the authors recommend evaluating assumption violations and model misfit based on their practical consequences. Not all assumption violations or sources of model misfit are equally serious. Violations of local independence, for example, can be substantively informative, often suggesting multidimensionality that may or may not need to be modeled. The discussion of when a model may be considered “unidimensional enough” for practical use brings together some of Reise’s most influential work, with strict unidimensionality being described as a mathematical ideal that rarely holds for real data. The authors provide concrete guidance for evaluating assumptions and illustrate each diagnostic tool using a real dataset. The chapter closes with a discussion of the difficulty of developing an overall goodness-of-fit test given the enormous number of possible response patterns, suggesting limited-information fit statistics as alternatives. It is rare for an introductory IRT text to offer such a practical and detailed guide to model evaluation; from my experience, this is exactly the type of information that applied researchers are most often seeking.

The Applications section (Section IV) addresses some of the practical considerations in fitting IRT models. Chapter 9 is more philosophical in nature, exploring the meaning of IRT trait scores. The authors show how IRT places persons and items on the same latent scale through several well-chosen analogies, and they discuss the challenges of assigning numerical values to latent constructs. Readers who regularly use scale scores in their own research may be especially interested in the results of a Monte Carlo simulation showing how IRT scores and summed scores computed from the same data can lead to different conclusions in downstream analyses. Chapter 10 combines three somewhat distinct topics—differential item functioning (DIF), computerized adaptive testing (CAT), and scale analysis—into a single chapter. The authors wisely avoid cataloging the dozens of available DIF procedures and instead focus on a single iterative approach, emphasizing graphical methods for evaluating practical impact rather than statistical significance alone. They also raise the possibility that much of the DIF observed on psychological scales may reflect multidimensionality and group mean differences rather than qualitative differences in item functioning. The CAT section is more conceptual and describes the advantages of CAT and some of the important design considerations. The authors illustrate both DIF and CAT applications using R, which is a major update from the first edition.

Embretson and Reise note that aside from the Patient-Reported Outcomes Measurement Information System (PROMIS), IRT has played a more limited role in scale development within psychology; it is more often used to analyze measures that already exist. They show how item information and category functioning can be used in scale development, once again cautioning against rules of thumb such as discrimination cutoffs for keeping or removing items. As someone who has collaborated on several scale development projects, I can attest that this temptation is common. I appreciated the authors’ critique of this practice and their warning that discarding items simply because of low discrimination may result in a scale that fails to capture important aspects of the construct. Chapter 11, the last chapter of this section, provides an overview of IRT-related software that is new to the second edition. Several widely used R packages are described, including mirt and sirt, as well as some of the newer commercial programs, such as flexMIRT. Syntax examples and screenshots make the chapter especially useful for new learners.

The final section of the book (Section V) covers advanced IRT models and includes two chapters new to the second edition: one on multidimensional IRT (MIRT; Chapter 12), the other on explanatory, mixture, and other advanced models (Chapter 13). Consistent with the theme of the book, Embretson and Reise describe each model in terms of what it reveals about both the construct and the people who differ on it. The MIRT chapter, which covers only compensatory models, presents both exploratory and confirmatory models for binary and polytomous data and shows how researchers can apply MIRT to better understand the internal structure of a construct. Several real data examples are used to illustrate how exploratory models can help identify meaningful dimensions and how confirmatory models test hypotheses about the factor structure. Readers working with longitudinal or developmental data will likely appreciate the discussion of models for learning and change, a topic that is increasingly important in practice but rarely covered in introductory texts. A particular strength of the chapter is that all confirmatory models, including the bifactor model, are presented within a unified framework. This organization helps readers connect what can otherwise seem like a large collection of unrelated models.

Chapter 13 provides a selective overview of explanatory, mixture, and response time models—as the authors note themselves, only a small sample of the many models that have been developed since the previous edition. As is true of the MIRT chapter, the focus is on how these models can be used to evaluate the response process and internal structure aspects of construct validity. The same abstract reasoning dataset is used throughout most of the chapter, which makes it easier for readers to see how different models can extract different types of information from the same responses. Explanatory IRT models such as the linear logistic test model (LLTM; Fischer, Reference Fischer1973) and the 2PL-constrained model (Embretson, Reference Embretson1999), as well as non-compensatory models such as the multicomponent latent trait model (MLTM; Whitely, Reference Whitely1980), are introduced as methods for decomposing the cognitive processes involved in responding to items. Mixture models with latent classes are then described as a method of accounting for population heterogeneity, allowing researchers to identify groups of respondents who may approach the same items in qualitatively different ways, such as through the use of different problem-solving strategies. The focus throughout the chapter is on how each model can be used to answer a different substantive question.

The chapter closes with an overview of response time models. Although the data example centers on van der Linden’s joint hierarchical model (van der Linden, Reference van der Linden2007), the authors also discuss some newer models that use response times to identify phenomena such as careless responding and item pre-knowledge. I appreciated that the empirical example showed that while incorporating response times did improve measurement precision, the practical gains were only modest. Findings like this are important to show because they remind readers that more complex models do not always lead to different substantive conclusions, something that is not frequently emphasized in methodological publications. All the empirical examples in Chapter 13 come from education and cognitive psychology. This is understandable given the origins of many explanatory and response time models; the LLTM and MLTM have their most natural applications to education, and response times are usually most relevant in cognitive assessment. Nevertheless, given the substantial number of clinical and health researchers who use this book, it would have been nice to see a psychopathology example of explanatory IRT with person-level covariates or a mixture IRT application showing how symptom patterns differ across latent classes. These types of examples would help readers see how advanced models can be applied to many of the measurement issues seen in psychological research more broadly.

The authors decided against including a final chapter on current and future directions, noting that they wished to stick to the fundamental principles of IRT. I certainly understand this decision. Including many more topics would push what is meant to be an introductory text toward a handbook or edited volume, which is not what the authors intended to write. Even so, there are some additions I would have enjoyed seeing. Given the large clinical audience of this book, a more complete introduction to IRT models for measuring unipolar constructs, one of Reise’s areas of expertise (e.g., Reise et al., Reference Reise, Du, Wong, Hubbard and Haviland2021), would likely be of interest to many readers. While the authors do introduce a limited number of IRT models for change, additional longitudinal applications and a short discussion of longitudinal DIF might also be helpful for social scientists who work with repeated-measures data. Finally, an online companion site with the datasets and R scripts would make it easier for readers to work through the examples and would likely increase the reach of an already widely read book.

In terms of classroom use, the book is well-suited for a single semester course in IRT, with each of its five sections covering roughly 2–4 weeks of material. Some of the earlier material, particularly the history of IRT and its connections to CTT, may be covered more quickly, whereas the more technical material and the sections on advanced models are likely to require additional time. Instructors may also wish to include some more advanced models that are not addressed in this text. The book would probably work best for courses that are taught using R. The generous presentation of R code also makes it a good resource for self-study, although readers with no prior experience in R may find it difficult to use as a stand-alone text.

Item Response Theory: Foundations for Psychologists and Social Scientists has all of the features that made the first edition such a useful resource for students and applied researchers wanting to learn the basics of IRT. The second edition integrates software implementation throughout most of the book, and the new chapters address several of the most important developments in IRT over the last 25 years. The data examples are detailed and relevant to readers from a wide range of social science backgrounds, and models are fit and interpreted in the context of substantive research questions. Embretson and Reise balance depth and breadth in a way that is well-suited for the more applied audience the book was written for. The book is rigorous but remains accessible to non-methodologists. Most importantly, it consistently reminds readers that ultimately, the goal of measurement is to better understand constructs and how people differ on them. It is difficult to imagine a better first book on IRT; this one will remain one of my top recommendations.