Multidimensional Item Response Theory

Cover -- Contents -- 1 Introduction -- 1.1 A Conceptual Framework for Thinking About People and Test Items -- 1.2 General Assumptions Behind Model Development -- 1.3 Exercises -- 2 Unidimensional Item Response Theory Models -- 2.1 Unidimensional Models of the Interactions of Persons and Test Items -- 2.1.1 Models for Items with Two Score Categories -- 2.1.2 Relationships Between UIRT Parameters and Classical Item Statistics -- 2.1.3 Models for Items with More Than Two Score Categories -- 2.2 Other Descriptive Statistics for Items and Tests -- 2.2.1 The Test Characteristic Curve -- 2.2.2 Information Function -- 2.3 Limitations of Unidimensional IRT Models -- 2.4 Exercises -- 3 Historical Background for Multidimensional Item Response Theory -- 3.1 Psychological and Educational Context for MIRT -- 3.2 Test Development Context for MIRT -- 3.3 Psychometric Antecedents of MIRT -- 3.3.1 Factor Analysis -- 3.3.2 Item Response Theory -- 3.3.3 Comparison of the Factor Analytic and MIRT Approaches -- 3.4 Early MIRT Developments -- 3.5 Developing Applications of MIRT -- 3.6 Influence of MIRT on the Concept of a Test -- 3.7 Exercises -- 4 Multidimensional Item Response Theory Models -- 4.1 Multidimensional Models for the Interaction Between a Person and a Test Item -- 4.1.1 MIRT Models for Test Items with Two Score Categories -- 4.1.2 MIRT Models for Test Items with More Than Two Score Categories -- 4.2 Future Directions for Model Development -- 4.3 Exercises -- 5 Statistical Descriptions of Item and Test Functioning -- 5.1 Item Difficulty and Discrimination -- 5.2 Item Information -- 5.3 MIRT Descriptions of Test Functioning -- 5.4 Summary and Conclusions -- 5.5 Exercises -- 6 Estimation of Item and Person Parameters -- 6.1 Background Concepts for Parameter Estimation -- 6.1.1 Estimation of the -vector with Item Parameters Known -- 6.2 Computer Programs for Estimating MIRT Parameters -- 6.2.1 TESTFACT -- 6.2.2 NOHARM -- 6.2.3 ConQuest -- 6.2.4 BMIRT -- 6.3 Comparison of Estimation Programs -- 6.4 Exercises -- 7 Analyzing the Structure of Test Data -- 7.1 Determining the Number of Dimensions for an Analysis -- 7.1.1 Over and Under-Specification of Dimensions -- 7.1.2 Theoretical Requirements for Fit by a One-Dimensional Model -- 7.2 Procedures for Determining the Required Number of Dimensions -- 7.2.1 DIMTEST -- 7.2.2 DETECT -- 7.2.3 Parallel Analysis -- 7.2.4 Difference Chi-Square -- 7.3 Clustering Items to Confirm Dimensional Structure -- 7.4 Confirmatory Analysis to Check Dimensionality -- 7.5 Concluding Remarks -- 7.6 Exercises -- 8 Transforming Parameter Estimates to a Specified Coordinate System -- 8.1 Converting Parameters from One Coordinate System to Another -- 8.1.1 Translation of the Origin of the -Space -- 8.1.2 Rotating the Coordinate Axes of the -Space -- 8.1.3 Changing the Units of the Coordinate Axes -- 8.1.4 Converting Parameters Using Translation, Rotation, and Change of Units -- 8.2 Recovering Transformations from Item- and Person-Parameters -- 8.2.1 Recovering Transformations from -vectors -- 8.2.2 Recovering Transformations Using Item Parameters -- 8.3 Transforming the -space for the Partially Compensatory Model -- 8.4 Exercises -- 9 Linking and Scaling -- 9.1 Specifying the Common Multidimensional Space -- 9.2 Relating Results from Different Test Forms -- 9.2.1.