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The theory and practice of item response theory, by Rafael Jaime de Ayala, New York, The Guilford Press, 2009, 448 pp., £41.00 (hardback), The theory and practice of item response theory has been written by an expert in item response theory (IRT) with the aim of reaching out to the research community to explain IRT, which is a widely used statistical method embraced by test developers. The author sets out to address both the 'how to' and 'why' of IRT. In tackling these questions, he contextualizes the theory by referring to an empirical dataset.The book contains 12 chapters. It is well organized with a very consistent format for each chapter. The concepts are arranged in a sequential way, moving from simple to complex to facilitate readers' understanding of the various IRT models. The chapter summary, at the end of each chapter, is a very effective way of enabling readers to recap on the key points, which have been discussed in the chapter.Chapter 1 provides an introduction to the concept of measurement with a brief explanation of the desirable properties of objective measurement and the different approaches to measurement such as IRT, classical test theory, and latent class analysis. Chapter 2 presents the Rasch model or one-parameter IRT model, which is the simplest model. The concept of the one-parameter IRT model sets out the rules for the more complicated models described in the subsequent chapters. This chapter also introduces the mathematical dataset that is used in the subsequent chapters. Chapters 3 and 4 present the concept of two different parameter estimation procedures and their application on the mathematical dataset. Chapter 3 assesses assumptions behind IRT such as undimimensionality and examines model-data fit with NOHARM and BIGSTEPS software. Chapter 4 presents the analysis of the dataset using the software BILOG and applying different parameter estimation techniques.Chapter 5 introduces the two-parameter IRT model, which takes into account the fact that items could discriminate between individuals and have different slopes. The dataset is reanalysed, and the model-data fit analysis is compared to the one-parameter IRT model. The development of the three-parameter model concept is presented in Chapter 6. The three parameters in this model are item location, item discrimination, and the pseudo-guessing. The dataset is reanalysed and the issues pertaining to model selection are discussed.Chapter 7 introduces the polytomous Rasch models, which consist of the rating scale model and the partial credit model. The next chapter addresses non-polytomous Rasch models, such as the generalized partial credit model and the graded response model. This is then followed by the conceptual development of two unordered polytomous models: the nominal response model and the multiple-choice model.The multidimensional model relating to more than one latent trait is presented in Chapter 10. The next chapter introduces the concepts of item linking and equating, which are useful for equating multiple forms and item ba...