Drawing on the work of internationally acclaimed experts in the field, this second volume in a three-volume set presents classical and modern statistical tools used in item response theory (IRT). "Based on scores in a battery of questions in Psychometrics, IRT is a paradigm for designing, analyzing, and interpreting the individual's abilities. Volume two covers mainly probability distributions, models with intentional and nuisance parameters, information criteria, and model identification issues, among others. To read through and comprehend the contents of this volume two, one needs calculus and mathematical statistics background. There are 20 well written chapters covering a range of topics?written by experts from all continents. The references in the chapters are exhaustive and up-to-date. I enjoyed reading this book. I recommend this book highly to economists, psychometricians, sociologists, marketing researchers, statistics and computing professionals." ~Journal of Statistical Computation and Simulation "(...)the 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 area of research because it describes a large variety of statistical techniques valuable in estimations for many other problems beyond IRT."~Stan Lipovetsky inTechnometrics,August 2021