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Elements of Adaptive Testing Theory and Practice

:	Wim J. van der Linden, Cees A. W. Glas
:	Wim J. van der Linden, Cees A.W. Glas
:	Elements of Adaptive Testing Theory and Practice
:	Springer-Verlag
:	9780387854618
:	1
:	CHF 129.60
:

:	Methoden der empirischen und qualitativen Sozialforschung
:	English

:	433
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

The arrival of the computer in educational and psychological testing has led to the current popularity of adaptive testing---a testing format in which the computer uses statistical information about the test items to automatically adapt their selection to a real-time update of the test taker's ability estimate. This book covers such key features of adaptive testing as item selection and ability estimation, adaptive testing with multidimensional abilities, sequencing adaptive test batteries, multistage adaptive testing, item-pool design and maintenance, estimation of item and item-family parameters, item and person fit, as well as adaptive mastery and classification testing. It also shows how these features are used in the daily operations of several large-scale adaptive testing programs.

	Preface	5
	Contributors	9
	Contents	11
	Part I Item Selection and Ability Estimation	14
	1 Item Selection and Ability Estimation in Adaptive Testing	15
	1.1 Introduction	15
	1.2 Classical Procedures	17
	1.2.1 Notation and Some Statistical Concepts	17
	1.2.2 Ability Estimators	19
	1.2.3 Choice of Estimator	20
	1.2.4 Classical Item-Selection Criteria	23
	1.3 Modern Procedures	24
	1.3.1 Maximum Global-Information Criterion	25
	1.3.2 Likelihood-Weighted Information Criterion	27
	1.3.3 Fully Bayesian Criteria	28
	1.3.4 Bayesian Criteria with Collateral Information	30
	1.3.5 Bayesian Criteria with Random Item Parameters	33
	1.3.6 Miscellaneous Criteria	35
	1.3.7 Evaluation of Item-Selection Criteria and Ability Estimators	36
	1.4 Concluding Remarks	39
	References	40
	2 Constrained Adaptive Testing with Shadow Tests	43
	2.1 Introduction	43
	2.2 Review of Existing Methods for Constrained CAT	45
	2.2.1 Item-Pool Partitioning	45
	2.2.2 Weighted-Deviation Method	45
	2.2.3 Maximum Priority Index Method	45
	2.2.4 Testlet-Based Adaptive Testing	46
	2.2.5 Multistage Testing	46
	2.2.6 Evaluation of Existing Approaches	47
	2.3 Constrained CAT with Shadow Tests	48
	2.4 Technical Implementation	49
	2.4.1 Basic Notation and Definitions	50
	2.4.2 IP Model for Shadow Test	51
	2.4.3 Numerical Aspects	53
	2.5 Four Applications to Adaptive Testing Problems	54
	2.5.1 CAT with Large Numbers of Nonstatistical Constraints	55
	2.5.2 CAT with Response-Time Constraints	55
	2.5.3 CAT with Item-Exposure Control	59
	2.5.4 CAT with Equated Number-Correct Scores	62
	2.6 Concluding Remarks	65
	References	65
	3 Principles of Multidimensional Adaptive Testing	68
	3.1 Introduction	68
	3.2 Literature Review	69
	3.3 Multidimensional Item Selection and Scoring	70
	3.3.1 Prior Density	71
	3.3.2 Likelihood Function	72
	3.3.3 Posterior Density	74
	3.3.4 Item Selection	76
	3.3.5 Posterior Inference	79
	3.4 Example	80
	3.4.1 Initialization	80
	3.4.2 Item Selection	81
	3.4.3 Provisional Ability Estimation	82
	3.4.4 Item Selection and Scoring Cycle	82
	3.5 Discussion	84
	3.6 Appendix: Computational Formulas	84
	References	85
	4 Multidimensional Adaptive Testing with Kullback–Leibler Information Item Selection	87
	4.1 Multidimensional IRT model	88
	4.2 Bayesian Estimation of bold0mu mumu *	89
	4.3 Kullback–Leibler Information	91
	4.3.1 Mutual Information	94
	4.4 Item Selection Using KL Information	94
	4.4.1 Posterior Expected Kullback–Leibler Information	95
	4.4.2 KL Distance between Subsequent Posteriors	97
	4.4.3 Mutual Information	98
	4.5 Relationship between Selection Criteria	99
	4.6 Special Status of Some of the Ability Parameters	101
	4.6.1 Nuisance Abilities	101
	4.6.2 Composite Ability	104
	4.7 Posterior Covariance	107
	4.8 Conclusion	109
	References	110
	5 Sequencing an Adaptive Test Battery	112
	5.1 Introduction	112
	5.2 Multilevel Model	114
	5.3 Empirical Bayes Approach	115
	5.3.1 Selection of Initial Pool	115
	5.3.2 Selection of First Test	117
	5.3.3 Administration of First Test	118
	5.3.4 Selection of Subsequent Tests	119
	5.3.5 Administration of Subsequent Tests	120
	5.4 Simulation Study	120
	5.4.1 Design of Study	121
	5.4.2 Results	122
	5.5 Concluding Remarks	125
	5.6 Appendix: Computational Approach	126
	References	127
	Part II Applications in Large-Scale Testing Programs	129
	6 Adaptive Tests for Measuring Anxiety and Depression	130
	6.1 Introduction	130
	6.2 Development of CAT Systems	132
	6.2.1 Patient Samples for Empirical Item Analyses	132
	6.2.2 Definition of Target Construct	133
	6.2.3 Initial Item Pool	133
	6.2.4 Test Dimensionality	134
	6.2.5 Nonparametric Analyses	134
	6.2.6 DIF Analysis	135
	6.2.7 Item Calibration	136
	6.2.8 Investigation of Model Fit	136
	6.2.9 Item Banks	137
	6.2.10 CAT Algorithm	137
	6.2.11 Delivery System	138
	6.3 Evaluation Studies	138
	6.4 Discussion	140
	References	141
	7 MATHCAT: A Flexible Testing System in Mathematics Education for Adults	144
	7.1 Introduction	144
	7.2 The Item Bank for Numerical and Mathematical Skills	145