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Contributions to latent variable modeling in educational measurement
Zwitser, R.J.
Publication date
2015
Document Version
Final published version
Link to publication
Citation for published version (APA):
Zwitser, R. J. (2015). Contributions to latent variable modeling in educational measurement.
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Contributions to Latent Variable
Modeling in Educational Measurement
Robert J. Zwitser
Contributions t
o Lat
ent V
ariable Modeling in Educational Measur
ement
Rober
.
.
Printed by Ipskamp Drukkers, Enschede
Graphic design cover by Rachel van Esschoten, DivingDuck Design Typeset with LATEX
ISBN: 978-94-6259-618-4
c
2015, Robert J. Zwitser. All rights reserved
.
Contributions to Latent Variable Modeling in
Educational Measurement
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam
op gezag van de Rector Magnificus prof. dr. D.C. van den Boom
ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel
op woensdag 22 april 2015, te 14:00 uur
door
Robert Johannes Zwitser
Promotiecommissie:
Promotor: Prof. dr. G.K.J. Maris Universiteit van Amsterdam
Overige leden: Dr. L.A. van der Ark Universiteit van Amsterdam
Prof. dr. D. Borsboom Universiteit van Amsterdam
Prof. dr. C.A.W. Glas Universiteit Twente
Prof. dr. H. Kelderman Vrije Universiteit
Prof. dr. S. Kreiner University of Copenhagen
Prof. dr. F.J. Oort Universiteit van Amsterdam
Contents
1 Introduction 1
1.1 The construct . . . 1
1.2 Latent variable models . . . 2
1.3 This thesis . . . 3
1.3.1 CML Inference with MST Designs . . . 3
1.3.2 The Nonparametric Rasch Model . . . 5
1.3.3 DIF in International Surveys . . . 5
1.4 Note about notation . . . 6
2 CML Inference with MST Designs 7 2.1 Conditional likelihood estimation . . . 10
2.1.1 Estimation of item parameters . . . 11
2.1.2 Comparison with alternative estimation procedures . . . 14
2.1.3 Estimation of person parameters . . . 16
2.2 Model fit . . . 17
2.2.1 Model fit in adaptive testing . . . 17
2.2.2 Likelihood ratio test . . . 19
2.2.3 Item fit test . . . 22
2.3 Examples . . . 23
2.3.1 Simulation . . . 24
2.3.2 Real data . . . 28
2.4 Discussion . . . 31
3 The Nonparametric Rasch Model 37 3.1 Introduction . . . 38
3.2.1 Parametric IRT models . . . 39
3.2.2 Nonparametric IRT models . . . 40
3.3 Sufficiency . . . 42
3.3.1 The existence of a sufficient statistic . . . 42
3.3.2 Ordinal sufficiency . . . 45
3.3.3 Nonparametric Rasch model . . . 51
3.4 Testable implications of ordinal sufficiency . . . 52
3.4.1 Example . . . 55
3.5 Discussion . . . 56
Appendix . . . 59
4 DIF in International Surveys 63 4.1 Introduction . . . 64
4.1.1 Remove DIF items and ignore DIF in the model . . . . 65
4.1.2 Add subpopulation-specific item parameters and compare person parameter estimates . . . 66
4.1.3 Add subpopulation-specific item parameters and adjust the observed total score . . . 69
4.1.4 DIF as an interesting outcome . . . 70
4.2 Method . . . 71
4.2.1 The construct . . . 71
4.2.2 Purpose of the measurement model . . . 71
4.2.3 Comparability . . . 72
4.2.4 Difference with existing methods . . . 72
4.2.5 Estimation process . . . 73
4.2.6 Plausible responses and plausible scores . . . 74
4.2.7 Model fit evaluation . . . 74
4.3 Data . . . 75
4.3.1 Data set 1 . . . 75
4.3.2 Data set 2 . . . 75
4.4 Illustrations and results . . . 76
4.4.1 Exploring the model fit . . . 77
4.4.2 Incomplete design . . . 79
4.4.3 A large data example . . . 80
5 Discussion 91
5.1 The optimal CAT for high-stakes testing . . . 91
5.2 To order, or not to order: that is the question . . . 93
5.3 We want DIF! . . . 94
Bibliography 97
References published chapters 105
Summary 107
Samenvatting 109
