1 Introduction
1.1 Overview of Rasch Measurement Theory
1.2 Online Resources
2 Dichotomous Rasch Model
2.1 Example Data: Transitive Reasoning Test
2.2 Dichotomous Rasch Model Analysis with CMLE in eRm
2.3 Dichotomous Rasch Model Analysis with MMLE in TAM
2.4 Dichotomous Rasch Model Analysis with JMLE in TAM
2.5 Example Results Section
2.6 Exercise
2.7 Supplementary Learning Materials
3 Evaluating the Quality of Measures
3.1 Evaluating Measurement Quality from the Perspective of Rasch Measurement Theory
3.2 Example Data: Transitive Reasoning Test
3.3 Rasch Model Fit Analysis with CMLE in eRm
3.4 Graphical Displays for Evaluating Model-Data Fit
3.4.1 Reliability
3.5 Rasch Model Fit Analysis with MMLE in TAM
3.6 Rasch Model Fit Analysis with JMLE in TAM
3.7 Exercise
4 Rating Scale Model
4.1 Example Data: Liking for Science
4.2 RSM Analysis with CMLE in eRm
4.3 RSM Analysis with MMLE in TAM
4.4 RSM Analysis with JMLE in TAM
4.5 Example Results Section
4.6 Exercise
5 Partial Credit Model
5.1 Example Data: Liking for Science
5.2 PCM Analysis with CMLE in eRm
5.3 Summarize the Results in Tables
5.4 PCM Application with MMLE in TAM
5.5 PCM Application with JMLE in TAM
5.6 Example results section
5.7 Exercise
6 Many Facet Rasch Model
6.1 Running the MFRM with Wide-Format Data in TAM Package
6.2 Another Example: Running PC-MFRM with Long-Format Data using the TAM Package
6.2.1 Specify the PC-MFRM
6.3 Notes on Formulations for Many-Facet Rasch Models
6.4 Example Results Section
6.5 Exercise
7 Basics of Differential Item Functioning
7.1 Detecting Differential Item Functioning in R for Dichotomous Items
7.1.1 Example Data: Transitive Reasoning
7.2 Detecting Differential Item Functioning in R for Polytomous Items
7.2.1 Example Data: Style Ratings
7.3 Exercise
Bibliography
Biography
Stefanie A. Wind is an Associate Professor of Educational Measurement at the University of Alabama. Her primary research interests include the exploration of methodological issues in the field of educational measurement, with emphases on methods related to rater-mediated assessments, rating scales, Rasch models, item response theory models, and nonparametric item response theory, as well as applications of these methods to substantive areas related to education.
Cheng Hua is a Ph.D. candidate in Educational Measurement program at the University of Alabama. His primary research interests include Rasch Measurement theory, advanced regression models, Bayesian statistics, and visual learning tools (such as Mind Maps and Concept Maps). He enjoys applying his psychometric and statistical skills to address real-world research questions through interdisciplinary collaborations.
Over 60 years ago, Georg Rasch introduced a fundamentally new way of viewing measurement theory into the social sciences. His approach to invariant measurement provides the opportunity to achieve sample-free calibration of items and item-free measurement of persons. His research remains the gold standard for developing psychometrically sound assessments. Stefanie A. Wind and Cheng Hua introduce Rasch's fundamental ideas to students, researchers, and practitioners using readily available software in R that facilitates the quest for invariant measurement.
-George Engelhard, University of Georgia
