This volume gathers together a set of extensions of the Rasch model, one of the most prominent models for measurement in educational research and - cial science developed by Danish mathematician Georg Rasch. The idea for this volume emerged during a meeting of the Psychometric Society in M- terey, CA. At that meeting, friends and colleagues discussed news about the impending retirement of Dr. Jurgen ¨ Rost, an important innovator and m- tor in this field. To recognize Jurgen’s ¨ contributions, we decided to produce a collection of research on extending the Rasch model as well as embedding the Rasch model in more complex statistical models, an area that is receiving broad interest in many fields of social sciences at the current time. This collection contains 22 chapters by recognized international experts in the field. The contributions cover topics ranging from general model extensions to application in fields as diverse as cognition, personality, organizational and sports psychology, and health sciences and education. The Rasch model is designed for categorical data, often collected as ex- inees’ responses to multiple tasks such as cognitive items from psychological tests or from educational assessments. The Rasch model’s elegant mathema- cal form is suitable for extensions that allow for greater—exibility in handling complex samples of examinees and collections of tasks from different domains. In these extensions, the Rasch model is enhanced by additional structural - ements that account either for differences between diverse populations or for differences among observed variables.