Intro
Foreword
Contents
Chapter 1: Introduction to Advances in Applications of Rasch Measurement in Science Education
1.1 Item Response Theory Models vs. Rasch Models
1.2 Theory of Construct
1.3 Sample Size for Rasch Analysis
1.4 Uses of Fit Statistics
1.5 Local Independence and Dimensionality
1.6 Wright Map
1.7 Linking Rasch Measures
1.8 Using Rasch Measures for Subsequent Analyses
References
Chapter 2: Rasch Measurement in Discipline-Based Physics Education Research
2.1 Motivation and Introduction
2.2 Scope and Structure of Review

2.3 Diverse Use of Rasch Measurement in Physics Education Research
2.3.1 Assessment Revalidation and Assessment Development
2.3.2 Diverse Constructs, Assessment Formats and Scoring Schemes
2.3.3 Diverse Models and Analytical Techniques
2.4 Confusions and Improper Practices of Rasch Measurement in Physics Education Research
2.4.1 Theory-Driven Nature of Rasch Measurement
2.4.2 Principles and Operations of Rasch Measurement
2.4.3 Confirmatory Bias in Practice
2.4.4 Inconsistent Benchmarks for Analysis
2.5 Discussion and Implication

Appendix: A Summary of Reviewed Studies of Rasch Measurement in Discipline-Based Physics Education Research
References
Chapter 3: Using R Software for Rasch Model Calibrations
3.1 Introduction
3.2 What Is R?
3.2.1 Installation of the R Software and RStudio
3.2.2 Loading Data
3.3 Rasch Model Applications in R
3.3.1 R Programs/Packages for Rasch Modeling
3.3.2 Package Installation
3.3.3 Unidimensional Rasch Application for Dichotomous Data (Using the ``eRm ́́package)
Fitting the Rasch Model
Item Parameter Estimation
Item Characteristic Curve (ICC)

Person Ability Parameter Estimation
Model Evaluation
3.3.4 Unidimensional Rasch Application for Polytomous Data (Using ``TAM ́́for PCM)
Fitting the Partial Credit Model
Item Parameter Estimation
Category Characteristic Curve
Person Ability Parameter Estimation
Model Evaluation
3.3.5 Multidimensional Rasch Application for Dichotomous Data (Using ``mirt)́́
Fitting the Two-Dimensional Rasch Model
Item Parameter Estimation
Item Characteristic Surface
Person Ability Parameter Estimation
Model Evaluation
Epilogue
R Code
References

Chapter 4: Bayesian Partial Credit Model and Its Applications in Science Education
4.1 Introduction
4.1.1 Rasch Measurement in Science Education
4.1.2 Different Estimation Approaches to Rasch Analyses in Science Education
4.1.3 The Bayesian Approach
4.1.4 Programme for International Student Assessment
4.2 Objectives
4.3 Methods
4.4 Formulation of the PCM in Stan
4.5 Data Simulation for Parameter Recovery
4.6 Empirical Application Results and Model Checking
4.7 Convergence and Efficiency Diagnostics
4.8 Estimated Parameters