Multivariate and Mixture Distribution Rasch Models

This volume covers extensions of the Rasch model, one of the most researched and applied models in educational research and social science. This collection contains 22 chapters by some of the most recognized international experts in the field. They cover topics ranging from general model extensions to applications 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 examinees' responses to multiple tasks such as cognitive items from psychological tests or from educational assessments. The Rasch model's elegant mathematical form is suitable for extensions that allow for greater flexibility in handling complex samples of examinees and collections of tasks from different domains. In these extensions, the Rasch model is enhanced by additional structural elements that either account for differences between diverse populations or for differences among observed variables.

Research on extending well-known statistical tools like regression, mixture distribution, and hierarchical linear models has led to the adoption of Rasch model features to handle categorical observed variables. We maintain both perspectives in the volume and show how these merged models-Rasch models with a more complex item or population structure-are derived either from the Rasch model or from a structural model, how they are estimated, and where they are applied.

Matthias von Davier is a Senior Research Scientist in the Research & Development Division at Educational Testing Service. He is the author of WINMIRA, a software package for estimating latent class models, mixture distribution Rasch models, and hybrid Rasch models. The software grew out of his work with colleagues at the Methodology Department of the Institute for Science Education (IPN) in Kiel, Germany. Von Davier's current research is concerned with extensions of Raschmodels and more general Item Response Theory (IRT) models to multidimensional, diagnostic models and with mixture distribution models, with statistical computation and estimation, and with applications of psychometric models in national and international educational assessments.

Claus H. Carstensen is a junior Professor in the Psychometrics and Methodology Department at the IPN, Carstensen's work is concerned with multidimensional extensions of the Rasch model and applications of these models in intelligence and expertise research and educational assessments. He and Juergen Rost, head of the IPN's Methodology Department at the time, developed MULTIRA, a software package for multidimensional Rasch models. Before his current position, Carstensen was a Research Officer at the Australian Council of Educational Research where his focus was large-scale data analysis using multidimensional extensions of the Rasch model.

Résumé
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.

Contenu
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 ModelsSpecific 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.