Multivariate and Mixture Distribution Rasch Models

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 ?eld. 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 ?elds of social sciences at the current time. This collection contains 22 chapters by recognized international experts in the?eld.Thecontributionscovertopicsrangingfromgeneralmodelextensions to application in ?elds 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 di?erent domains. In these extensions, the Rasch model is enhanced by additional structural - ements that account either for di?erences between diverse populations or for di?erences among observed variables.

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 ?eld. 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 ?elds of social sciences at the current time. This collection contains 22 chapters by recognized international experts in the?eld.Thecontributionscovertopicsrangingfromgeneralmodelextensions to application in ?elds 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 di?erent domains. In these extensions, the Rasch model is enhanced by additional structural - ements that account either for di?erences between diverse populations or for di?erences among observed variables.

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 ?eld. 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 ?elds of social sciences at the current time. This collection contains 22 chapters by recognized international experts in the?eld.Thecontributionscovertopicsrangingfromgeneralmodelextensions to application in ?elds 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 di?erent domains. In these extensions, the Rasch model is enhanced by additional structural - ements that account either for di?erences between diverse populations or for di?erences among observed variables.

Introduction: Extending the Rasch Model.- Introduction: Extending the Rasch Model.- Multivariate and Mixture Rasch Models.- Measurement Models as Narrative Structures.- Testing Generalized Rasch Models.- The Mixed-Coefficients Multinomial Logit Model: A Generalized Form of the Rasch Model.- Loglinear Multivariate and Mixture Rasch Models.- Mixture-Distribution and HYBRID Rasch Models.- Generalized Models—Specific Research Questions.- Application of the Saltus Model to Stagelike Data: Some Applications and Current Developments.- Determination of Diagnostic Cut-Points Using Stochastically Ordered Mixed Rasch Models.- A HYBRID Model for Test Speededness.- Multidimensional Three-Mode Rasch Models.- (Almost) Equivalence Between Conditional and Mixture Maximum Likelihood Estimates for Some Models of the Rasch Type.- Rasch Models for Longitudinal Data.- The Interaction Model.- Multilevel Rasch Models.- Applications of Multivariate and Mixed Rasch Models.- Mixed Rasch Models for Measurement in Cognitive Psychology.- Detecting Response Styles and Faking in Personality and Organizational Assessments by Mixed Rasch Models.- Application of Multivariate Rasch Models in International Large-Scale Educational Assessments.- Studying Development via Item Response Models: A Wide Range of Potential Uses.- A Comparison of the Rasch Model and Constrained Item Response Theory Models for Pertinent Psychological Test Data.- Latent-Response Rasch Models for Strategy Shifts in Problem-Solving Processes.- Validity and Objectivity in Health-Related Scales: Analysis by Graphical Loglinear Rasch Models.- Applications of Generalized Rasch Models in the Sport, Exercise, and the Motor Domains.