Multidimensional Item Response Theory (eBook)

Preface 5
Contents 7
Introduction 10
1.1 A Conceptual Framework for Thinking About People and Test Items 12
1.2 General Assumptions Behind Model Development 17
1.3 Exercises 19
Unidimensional Item Response Theory Models 20
2.1 Unidimensional Models of the Interactions of Persons and Test Items 20
2.2 Other Descriptive Statistics for Items and Tests 52
2.3 Limitations of Unidimensional IRT Models 62
2.4 Exercises 63
Historical Background for Multidimensional Item Response Theory 65
3.1 Psychological and Educational Context for MIRT 68
3.2 Test Development Context for MIRT 69
3.3 Psychometric Antecedents of MIRT 71
3.4 Early MIRT Developments 79
3.5 Developing Applications of MIRT 82
3.6 Influence of MIRT on the Concept of a Test 83
3.7 Exercises 84
Multidimensional Item Response Theory Models 86
4.1 Multidimensional Models for the Interaction Between a Person and a Test Item 92
4.2 Future Directions for Model Development 117
4.3 Exercises 118
Statistical Descriptions of Item and Test Functioning 120
5.1 Item Difficulty and Discrimination 120
5.2 Item Information 128
5.3 MIRT Descriptions of Test Functioning 131
5.4 Summary and Conclusions 140
5.5 Exercises 141
Estimation of Item and Person Parameters 143
6.1 Background Concepts for Parameter Estimation 144
6.2 Computer Programs for Estimating MIRT Parameters 154
6.3 Comparison of Estimation Programs 181
6.4 Exercises 182
Analyzing the Structure of Test Data 185
7.1 Determining the Number of Dimensions for an Analysis 185
7.2 Procedures for Determining the Required Number of Dimensions 207
7.3 Clustering Items to Confirm Dimensional Structure 226
7.4 Confirmatory Analysis to Check Dimensionality 230
7.5 Concluding Remarks 234
7.6 Exercises 235
Transforming Parameter Estimates to a Specified Coordinate System 238
8.1 Converting Parameters from One Coordinate System to Another 240
8.2 Recovering Transformations from Item- and Person- Parameters 266
8.3 Transforming the ™-space for the PartiallyCompensatory Model 274
8.4 Exercises 276
Linking and Scaling 279
9.1 Specifying the Common Multidimensional Space 280
9.2 Relating Results from Different Test Forms 290
9.3 Estimating Scores on Constructs 305
9.4 Summary and Discussion 312
9.5 Exercises 313
Computerized Adaptive Testing Using MIRT 315
10.1 Component Parts of a CAT Procedure 315
10.2 Generalization of CAT to the Multidimensional Case 317
10.3 Future Directions for MIRT-CAT 341
10.4 Exercises 342
References 344
Index 351