Drawing on the work of internationally acclaimed experts in the field, this first volume in a three-volume set presents all major item response models. It covers many model developments that have occurred in the field during the last 20 years. "Handbook I is likely to be useful for undergraduate or graduate students who have an interest in pursuing quantitative research in educational and psychological testing, especially with datasets that contain multiple discrete outcomes. Master- and doctoral-level students seeking dissertation topics and doing literature reviews will find Handbook I a valuable resource."~Edward H. Ip, Wake Forest School of Medicine, Journal of the American Statistical Association "Based on scores in a battery of questions in Psychometrics, IRT is a paradigm for designing, analyzing, and interpreting the individual's abilities. Volume one describes models that are used in IRT. Basic knowledge of calculus and statistical theory are necessary to understand the contents of volume one. The references are thorough and up-to-date?I enjoyed reading this book. I recommend this book to psychologists, sociologists, statistics and computing professionals."~Journal of Statistical Computation and Simulation "This handbook presents a huge compendium of models which could be innovative even for specialists in IRT and related applied research. It can definitely be useful for lecturers and graduate students, researchers and practitioners in applied psycho-sociological projects. Actually, it can be useful in much wider than just IRT related area of research, because it describes a large variety of statistical ideas and methods valuable in estimations for many other problems as well."~Stan Lipovetsky inTechnometrics, August 2021