Multivariate and Mixture Distribution Rasch Models: Extensions and Applications

✍ Scribed by Matthias von Davier (auth.), Claus H. Carstensen (eds.)

• Publisher: Springer-Verlag New York
• Year: 2007
• Tongue: English
• Leaves: 397
• Series: Statistics for Social and Behavioral Sciences
• Edition: 1
• Category: Library

✦ Synopsis

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 Rasch models 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.

✦ Table of Contents

Front Matter....Pages I-XVIII
Introduction: Extending the Rasch Model....Pages 1-12
Front Matter....Pages 13-13
Measurement Models as Narrative Structures....Pages 15-35
Testing Generalized Rasch Models....Pages 37-55
The Mixed-Coefficients Multinomial Logit Model: A Generalized Form of the Rasch Model....Pages 57-75
Loglinear Multivariate and Mixture Rasch Models....Pages 77-97
Mixture-Distribution and HYBRID Rasch Models....Pages 99-115
Front Matter....Pages 117-117
Application of the Saltus Model to Stagelike Data: Some Applications and Current Developments....Pages 119-130
Determination of Diagnostic Cut-Points Using Stochastically Ordered Mixed Rasch Models....Pages 131-146
A HYBRID Model for Test Speededness....Pages 147-156
Multidimensional Three-Mode Rasch Models....Pages 157-175
(Almost) Equivalence Between Conditional and Mixture Maximum Likelihood Estimates for Some Models of the Rasch Type....Pages 177-189
Rasch Models for Longitudinal Data....Pages 191-199
The Interaction Model....Pages 201-216
Multilevel Rasch Models....Pages 217-232
Front Matter....Pages 233-233
Mixed Rasch Models for Measurement in Cognitive Psychology....Pages 235-253
Detecting Response Styles and Faking in Personality and Organizational Assessments by Mixed Rasch Models....Pages 255-270
Application of Multivariate Rasch Models in International Large-Scale Educational Assessments....Pages 271-280
Studying Development via Item Response Models: A Wide Range of Potential Uses....Pages 281-292
A Comparison of the Rasch Model and Constrained Item Response Theory Models for Pertinent Psychological Test Data....Pages 293-309
Latent-Response Rasch Models for Strategy Shifts in Problem-Solving Processes....Pages 311-328
Front Matter....Pages 233-233
Validity and Objectivity in Health-Related Scales: Analysis by Graphical Loglinear Rasch Models....Pages 329-346
Applications of Generalized Rasch Models in the Sport, Exercise, and the Motor Domains....Pages 347-356
Erratum....Pages E1-E1
Back Matter....Pages 357-398

✦ Subjects

Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Education (general); Psychometrics; Quality of Life Research; Psychological Methods/Evaluation