Applying the Rasch Model

Trevor G. Bond is currently Adjunct Professor at the College of Arts, Society and Education at James Cook University, Australia. Zi Yan is Associate Professor in the Department of Curriculum and Instruction at the Education University of Hong Kong. Moritz Heene is Full Professor of Learning Sciences Research Methodologies (i.e., Quantitative Methods) at the Ludwig-Maximilians-Universität München, Germany.

Foreword

Preface

Notes on This Volume

About the Authors






Why Measurement Is Fundamental
Children Can Construct Measures

Interval Scales v. Ratio Scales: A Conceptual Explanation

Statistics and/or Measurement

Why Fundamental Measurement?

Derived Measures

Conjoint Measurement

The Rasch Model for Measurement

A More Suitable Analogy for Measurement in the Human Sciences

In Conclusion

Summary




Important Principles of Measurement Made Explicit
An example: "By How Much?"

Moving From Observations to Measures

Summary




Basic Principles of the Rasch Model
The Pathway Analogy

A Basic Framework for Measurement

The Rasch Model

Summary




Building a Set of Items for Measurement
The Nature of the Data

Analyzing Dichotomous Data: The BLOT

A Simple Rasch Summary: The Item Pathway

Item Statistics

Item Fit

The Wright Map

Targeting

Comparing Persons and Items

Summary

Extended Understanding

The Problem of Guessing

Difficulty, Ability, and Fit

The Theory–Practice Dialog

Summary




Invariance: A Crucial Property of Scientific Measurement
Person and Item Invariance

Common-Item Linking

Please Keep in Mind

Anchoring Item Values

Vertical Scaling

Common-Person Linking

Invariance of Person Estimates across Tests: Concurrent Validity

The PRTIII-Pendulum

Common-Person Linking: BLOT & PRTIII

The Theory–Practice Dialog

Measurement Invariance: Where It Really Matters

Failures of Invariance: DIF

Differential Rater Functioning

DIF: Not Just a Problem, but an Opportunity

Summary




Measurement Using Likert Scales
The Rasch Model for Polytomous Data

Analyzing Rating Scale Data: The Instrumental Attitude towards Self-Assessment Questionnaire

Summary

Extended Understanding

Summary




The Partial Credit Rasch Model
Clinical Interview Analysis: A Rasch-Inspired Breakthrough

Scoring Interview Transcripts

Partial Credit Model Results

Interpretation

The Theory–Practice Dialog

Summary

Extended Understanding

Point–Measure Correlations

Fit Statistics

Dimensionality: Primary Components Factor Analysis

Summary




Measuring Facets Beyond Ability and Difficulty
A Basic Introduction to the Many-Facets Rasch Model

Why Not Use Interrater Reliability?

Relations Among the Rasch Family of Models

Data Specifications of the Many-Facets Rasch Model

Rating Creativity of Junior Scientists

8.6 Many-Facets Analysis of Eighth-Grade Writing

Summary

Extended Understanding

Rasch Measurement of Facets Beyond Rater Effects

Summary




Making Measures, Setting Standards, and Rasch Regression
Creating a Measure from Existing Data: The RMPFS (Zi Yan, EdUHK)

Method: Data

Physical Fitness Indicators

Data Analysis

Seven Criteria to Investigate the Quality of Physical Fitness Indicators

Results and Discussion

Optimising Response Categories

Influence of Underfitting Persons on the RMPFS

Properties of the RMPFS With Subsamples

Age Dependent or Age Related?

The Final Version of RMPFS

Objective Standard Setting: The OSS Model (Gregory Stone, U Toledo)

Early Definitions

The Objective Standard Setting Models

Objective Standard Setting for Dichotomous Examinations

Objective Standard Setting for Judge-Mediated Examinations

Fair Standards, Not Absolute Values

Rasch Regression (Svetlana Beltyukova, U Toledo)

Predicting Physician Assistant Faculty Intention to Leave Academia

Rasch Regression Using the Anchored Formulation

Rasch Regression: Alternative Approaches

Discussion

Summary




The Rasch Model Applied Across the Human Sciences
Rasch Measurement in Health Sciences

Optimising an Existing Instrument: The NIHSS and a Central Role for PCA

Creating a Short Form of an Existing Instrument: The FSQ

FSQ-SF

Theory Guides Assessment Revisions: The PEP–S8

Applications in Education and Psychology

Rasch Measures as Grist for the Analytical Mill

Rasch Gain Calculations: Racking and Stacking

Rasch Learning Gain Calculations: The CCI

Racking and Stacking

Stacking Can Be Enough: UPAM

Sub- Test Structure Informs Scoring Models

Applications to Classroom Testing

Can Rasch Measurement Help S.S. Stevens?

Using Rasch Measures with Path Analysis (SEM Framework)

Rasch Person Measures Used in a Partial Least Squares (PLS) Framework

And Those Rasch Measurement SEs?

Can We Really Combine SEM and Rasch Models?

Conclusion

Summary




Rasch Modeling Applied: Rating Scale Design
Rating Scale Design

Category Frequencies and Average Measures

Thresholds and Category Fit

Revising a Rating Scale

An Example

Guidelines for Collapsing Categories

Problems With Negatively Worded Items

The Invariance of the Measures across Groups

Summary




Rasch Model Requirements: Model Fit and Unidimensionality
The Data, the Model, and the Residuals

Residuals

Fit Statistics

Expectations of Variation

Fit, Misfit, and Interpretation

Fit: Issues for Resolution

Principal Components Analysis of Rasch Residuals: The BLOT as an Exemplar

One Dimension, Two Dimensions, Three Dimensions, More?

Extended Understanding

A Further Investigation: BLOT and PRTIII

Summary




A Synthetic Overview

Additive Conjoint Measurement (ACM)

True Score Theory, Latent Traits, and Item Response Theory

Would You Like an Interval Scale With That?

Model Assumptions and Measurement Requirements

Construct Validity

The Rasch Model and Progress of Science

Back to the Beginning and Back to the End

Summary

Appendix A: Getting Started

Appendix B: Technical Aspects of the Rasch Model

Appendix C: Going All the Way

Glossary

Author Index

Subject Index