Essays on Item Response Theory

by Boomsma, Anne; Van Duijn, Marijtje A. J.; Snijders, Tom A. B.

• ISBN13: 9780387951478
• ISBN10: 0387951474
• Format: Paperback
• Copyright: 2000-11-01
• Publisher: Springer Nature

Summary

This collection of papers provides an up to date treatment of item response theory, an important topic in educational testing.

Table of Contents

Preface	vii
I Parametric Item Response Theory
The Life of George Rasch as a Mathematician and as a Statistician	3	(22)
Erling B. Andersen
Lina Wøhlk Olsen
Introduction	3	(1)
Early Life (1901--1945)	4	(4)
Rasch's First Analysis of an Intelligence Test (1945--1948)	8	(2)
The Analysis of Slow Readers (1952)	10	(3)
Measuring Intelligence (1952--1953)	13	(2)
Discovery of the Dichotomous Rash Model (1952--1958)	15	(1)
Work on the Models (1953--1958)	16	(1)
The Conversation with Ragnar Frisch in 1959	17	(1)
Two Important Publications (1960 and 1961)	18	(3)
Last Years (1962--1980)	21	(2)
Epilogue	23	(2)
References	23	(2)
The Growing Family of Rasch Models	25	(18)
Jurgen Rost
Introduction	25	(1)
What Is a Rasch Model?	26	(4)
Some Historic Tracks of Generalizing the Rasch Model	30	(6)
A Hierarchical Structure of Generalized Rasch Models	36	(7)
References	37	(6)
Gain Scores Revisited Under an IRT Perspective	43	(26)
Gerhard H. Fischer
Introduction	43	(3)
Measuring Change on the Basis of a PCM	46	(4)
Some Technical Considerations	50	(2)
Statistical Assessment of Change Under a One-Sided H1	52	(3)
Statistical Assessment of Change Under a Two-Sided H1	55	(4)
An Example	59	(5)
Conclusion	64	(5)
References	66	(3)
Modeling Learning in Short-Term Learning Tests	69	(20)
Karl Christoph Klauer
Hubert Sydow
Introduction	69	(3)
The Learning Model	72	(2)
Estimating the Model	74	(1)
Validating the Model	74	(2)
Application	76	(8)
Discussion	84	(5)
References	86	(3)
An IRT Model for Multiple Raters	89	(20)
Norman D. Verhelst
Huub H.F.M. Verstralen
Introduction	89	(2)
The Model	91	(2)
A Multilevel Interpretation of the Model	93	(3)
The IRT Approach	96	(3)
The Consequences of Ignoring Dependencies	99	(5)
Conclusion	104	(5)
References	106	(3)
Conditional Independence and Differential Item Functioning in the Two-Parameter Logistic Model	109	(22)
Herbert Hoijtink
Introduction	109	(3)
A Statistic for Violations of Conditional Independence	112	(2)
A Statistic for Differential Item Functioning	114	(2)
The Posterior Predictive Distribution of Fit Statistics	116	(1)
Performance of Fit Statistics: A Small Simulation Study	117	(2)
Example: Masculinity and Femininity	119	(5)
Discussion	124	(1)
Appendix: Implementation of the Gibbs Sampler	125	(6)
References	127	(4)
Differential Item Functioning Depending on General Covariates	131	(18)
Cees A. W. Glas
Introduction	131	(2)
Modeling Differential Item Functioning	133	(2)
Evaluation of Differential Item Functioning	135	(1)
The MML Framework	136	(2)
A Power Study	138	(4)
A Comparison of the MH and LM Approach	142	(3)
Discussion	145	(4)
References	145	(4)
Statistical Tests for Differential Test Functioning in Rasch's Model for Speed Tests	149	(14)
Margo G.H. Jansen
Cees A.W. Glas
Introduction	149	(2)
An IRT Model for Response Times	151	(1)
Estimation	152	(2)
Model Tests	154	(1)
A Lagrange Multiplier Test for DTF	155	(1)
A Simulation Study	156	(2)
An Empirical Example	158	(2)
Discussion	160	(3)
References	161	(2)
Expected Response Functions	163	(10)
Charles Lewis
Introduction	163	(1)
Theoretical Development of ERFs	164	(1)
ERFs for the Rasch Model	165	(8)
References	170	(3)
A Logistic IRT Model for Decreasing and Increasing Item Characteristic Curves	173	(20)
Edwin L. Klinkenberg
Introduction	173	(1)
Attitudes on Issues	174	(2)
The Signed One-Parameter Logistic Model	176	(3)
The PARELLA Model	179	(1)
The Traffic Data	180	(6)
Summary and Discussion	186	(1)
Appendix: Estimating Equations of the Signed OPLM	187	(6)
References	190	(3)
Using Parameter Expansion to Improve the Performance of the EM Algorithm for Multidimensional IRT Population-Survey Models	193	(12)
Donald B. Rubin
Neal Thomas
Educational Assessment Surveys Using IRT Models	193	(1)
EM and PX-EM	194	(2)
Statistical Model	196	(4)
Example	200	(2)
Summary	202	(3)
References	203	(2)
Cross-Validating Item Parameter Estimation in Adaptive Testing	205	(16)
Wim J. van der Linden
Cees A.W. Glas
Introduction	205	(3)
Capitalization on Item Calibration Error	208	(3)
Cross-Validating Item Parameter Estimation	211	(2)
Empirical Study	213	(4)
Concludig Remarks	217	(4)
References	218	(3)
Imputation of Missing Scale Data with Item Response Models	221	(26)
Mark Huisman
Ivo W. Molenaar
Introduction	221	(1)
Incomplete Testing Designs	222	(2)
Imputation of Missing Item Responses	224	(5)
Effects of Imputation: A Simulation Study	229	(8)
Incomplete Designs versus Imputation	237	(4)
Summary and Conclusions	241	(6)
References	243	(4)
II Nonparametric Item Response Theory
On the Interplay Between Nonparametric and Parametric IRT, with Some Thoughts About the Future	247	(30)
Brian Junker
Introduction	247	(1)
Nonparametric IRT: Scale Construction	248	(4)
Parametric IRT: Modeling Dependence	252	(5)
Measurement Challenges Posed by Cognitive and Embedded Assessments	257	(20)
References	267	(10)
Reversibility Revisited and Other Comparisons of Three Types of Polytomous IRT Models	277	(20)
Bas T. Hemker
Introduction	277	(1)
Three Types of Models for Polytomous Items	278	(4)
Summary of Comparison Studies	282	(2)
The Three Types of Models and Reversibility	284	(5)
Comparison on Psychological Agreement	289	(4)
Discussion	293	(4)
References	294	(3)
Progress in NIRT Analysis of Polytomous Item Scores: Dilemmas and Practical Solutions	297	(22)
Klaas Sijtsma
L. Andries van der Ark
Mokken Scale Analysis for Polytomous Item Scores	297	(6)
Three Open Theoretical Problems in NIRT	303	(11)
Discussion	314	(5)
References	315	(4)
Two-Level Nonparametric Scaling for Dichotomous Data	319	(20)
Tom A.B. Snijders
Introduction	319	(2)
A Two-Level Model for Nonparametric Scaling of Dichotomous Data	321	(2)
Scalability Coefficients	323	(3)
Interpretation of Scalability Coefficients	326	(1)
Estimation of Scalability Coefficients	327	(1)
Object Scores	328	(1)
Reliability	329	(2)
Examples for Simulated Data	331	(2)
Example: Assessment of Teachers by Pupils	333	(2)
Discussion	335	(2)
Appendix: Proof that Between-Subject Scalability Coefficients Are Not Larger Than Within-Subject Coefficients	337	(2)
References	337	(2)
The Circles of Our Minds: A Nonparametric IRT Model for the Circumplex	339	(18)
Robert J. Mokken
Wijbrandt H. van Schuur
Ard Jan Leeferink
Introduction	339	(2)
The Circumplex Scale	341	(3)
A Search Procedure for a Circumplex Scale	344	(6)
Parameter Estimation: A Scale Scoring Method	350	(2)
Model Fit	352	(1)
Discussion	353	(4)
References	354	(3)
Using Resampling Methods to Produce an Improved DIMTEST Procedure	357	(20)
William Stout
Army Goodwin Froelich
Furong Gao
Introduction	357	(4)
Review of the DIMTEST Procedure	361	(4)
Correcting the Bias in TL	365	(1)
New Bias Correction Method	366	(2)
DIMTEST Without AT2	368	(2)
Monte Carlo Simulation Study	370	(3)
Discussion and Conclusions	373	(4)
References	374	(3)
Person Fit Across Subgroups: An Achievement Testing Example	377	(14)
Rob R. Meijer
Edith M.L.A. van Krimpen-Stoop
Introduction	377	(2)
Person Fit in IRT Models	379	(3)
Empirical Research with Person-Fit Statistics	382	(1)
An Empirical Example	383	(4)
Discussion	387	(4)
References	388	(3)
Single-Peaked or Monotone Tracelines? On the Choice of an IRT Model for Scaling Data	391	(24)
Wendy J. Post
Marijtje A.J. van Duijn
Berna van Baarsen
Introduction	391	(1)
Choosing an IRT Model	392	(2)
Monotone versus Single-Peaked Tracelines	394	(6)
Reanalysis of the Loneliness Scale Data	400	(9)
Summary and Discussion	409	(6)
References	411	(4)
Outline of Faceted Theory of Item Response Data	415	(18)
Gideon J. Mellenbergh
Introduction	415	(1)
Stimulus Facets	416	(3)
Person Facets	419	(1)
Recording Type Facet	420	(1)
Scaling Type Facet	420	(1)
Nested Facets	421	(3)
TIR and IRT	424	(3)
Example	427	(2)
Conclusion	429	(4)
References	430	(3)
Index	433	(6)
Abbreviations	439