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E-grāmata: Rasch Related Models and Methods for Health Science [Wiley Online]

Edited by (University of Copenhagen, Denmark), Edited by (University Pierre and Marie Curie, Paris, France), Edited by (Universite Pierre et Marie Curie, Paris 6, France)
  • Formāts: 384 pages
  • Sērija : ISTE
  • Izdošanas datums: 14-Dec-2012
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1118574451
  • ISBN-13: 9781118574454
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Rasch Related Models and Methods for Health SciencePalielināt
  • Formāts: 384 pages
  • Sērija : ISTE
  • Izdošanas datums: 14-Dec-2012
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1118574451
  • ISBN-13: 9781118574454
Citas grāmatas par šo tēmu:
Wiley Online E-booksMore info about Wiley Online
Rokasgrāmatas mājas lapa: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118574454
"The family of statistical models known as Rasch models started with a simple model for responses to questions in educational tests presented together with a number of related models that the Danish mathematician Georg Rasch referred to as models for measurement. Since the beginning of the 1950s the use of Rasch models has grown and spread from education to the measurement of health status. This book contains a comprehensive overview of the statistical theory of Rasch models."--Back cover.

The family of statistical models known as Rasch models started with a simple model for responses to questions in educational tests presented together with a number of related models that the Danish mathematician Georg Rasch referred to as models for measurement. Since the beginning of the 1950s the use of Rasch models has grown and has spread from education to the measurement of health status. This book contains a comprehensive overview of the statistical theory of Rasch models.
Part 1 contains the probabilistic definition of Rasch models, Part 2 describes the estimation of item and person parameters, Part 3 concerns the assessment of the data-model fit of Rasch models, Part 4 contains applications of Rasch models, Part 5 discusses how to develop health-related instruments for Rasch models, and Part 6 describes how to perform Rasch analysis and document results.

Preface xv
Karl Bang Christensen
Svend Kreiner
Mounir Mesbah
Part 1 PROBABILISTIC MODELS
1(42)
Chapter 1 The Rasch Model for Dichotomous Items
5(22)
Svend Kreiner
1.1 Introduction
5(7)
1.1.1 Original formulation of the model
5(4)
1.1.2 Modern formulations of the model
9(1)
1.1.3 Psychometric properties
10(1)
1.1.3.1 Requirements of IRT models
11(1)
1.2 Item characteristic curves
12(1)
1.3 Guttman errors
12(1)
1.4 Test characteristic curve
13(1)
1.5 Implicit assumptions
13(1)
1.6 Statistical properties
14(4)
1.6.1 The distribution of the total score
15(1)
1.6.2 Symmetrical polynomials
16(1)
1.6.3 Partial credit model parameterization of the score distribution
17(1)
1.6.4 Rasch models for subscores
17(1)
1.7 Inference frames
18(2)
1.8 Specific objectivity
20(1)
1.9 Rasch models as graphical models
21(1)
1.10 Summary
22(2)
1.11 Bibliography
24(3)
Chapter 2 Rasch Models for Ordered Polytomous Items
27(16)
Mounir Mesbah
Svend Kreiner
2.1 Introduction
27(6)
2.1.1 Example
27(1)
2.1.2 Ordered categories
28(3)
2.1.3 Properties of the polytomous Rasch model
31(2)
2.1.4 Assumptions
33(1)
2.2 Derivation from the dichotomous model
33(4)
2.3 Distributions derived from Rasch models
37(4)
2.3.1 The score distribution
39(1)
2.3.2 Conditional distribution of item responses given the total score
40(1)
2.4 Bibliography
41(2)
Part 2 INFERENCE IN THE RASCH MODEL
43(36)
Chapter 3 Estimation of Item Parameters
49(14)
Karl Bang Christensen
3.1 Introduction
49(2)
3.2 Estimation of item parameters
51(8)
3.2.1 Estimation using the conditional likelihood function
52(2)
3.2.2 Pairwise conditional estimation
54(2)
3.2.3 Marginal likelihood function
56(1)
3.2.4 Extended likelihood function
57(1)
3.2.5 Reduced rank parameterization
58(1)
3.2.6 Parameter estimation in more general Rasch models
59(1)
3.3 Example
59(1)
3.4 Bibliography
60(3)
Chapter 4 Person Parameter Estimation and Measurement in Rasch Models
63(16)
Svend Kreiner
Karl Bang Christensen
4.1 Introduction and notation
63(2)
4.2 Maximum likelihood estimation of person parameters
65(1)
4.3 Item and test information functions
66(1)
4.4 Weighted likelihood estimation of person parameters
67(1)
4.5 Example
67(3)
4.6 Measurement quality
70(6)
4.6.1 Reliability in classical test theory
70(1)
4.6.2 Reliability in Rasch models
71(2)
4.6.3 Expected measurement precision
73(1)
4.6.4 Targeting
74(2)
4.7 Bibliography
76(3)
Part 3 CHECKING THE RASCH MODEL
79(80)
Chapter 5 Item Fit Statistics
83(22)
Karl Bang Christensen
Svend Kreiner
5.1 Introduction
83(1)
5.2 Rasch model residuals
84(9)
5.2.1 Notation
84(2)
5.2.2 Individual response residuals: outfits and infits
86(1)
5.2.3 Problem 1: the distribution of outfit and infit test statistics
87(1)
5.2.4 Problem 2: calculating Evi
88(2)
5.2.5 Group residuals
90(1)
5.2.6 Group residuals for analysis of homogeneity
91(2)
5.3 Molenaar's U
93(1)
5.4 Analysis of item-restscore association
94(2)
5.5 Group residuals and analysis of DIF
96(1)
5.6 Kelderman's conditional likelihood ratio test of no DIF
96(2)
5.7 Test for conditional independence in three-way tables
98(2)
5.8 Discussion and recommendations
100(2)
5.8.1 Technical issues
100(1)
5.8.2 What to do when items do not agree with the Rasch model
101(1)
5.9 Bibliography
102(3)
Chapter 6 Overall Tests of the Rasch Model
105(6)
Svend Kreiner
Karl Bang Christensen
6.1 Introduction
105(1)
6.2 The conditional likelihood ratio test
105(4)
6.3 Other overall tests of fit
109(1)
6.4 Bibliography
109(2)
Chapter 7 Local Dependence
111(20)
Ida Marais
7.1 Introduction
111(2)
7.1.1 Reduced rank parameterization model for subtests
112(1)
7.1.2 Reliability indices
112(1)
7.2 Local dependence in Rasch models
113(1)
7.2.1 Response dependence
113(1)
7.3 Effects of response dependence on measurement
114(4)
7.4 Diagnosing and detecting response dependence
118(9)
7.4.1 Item fit
118(2)
7.4.2 Item residual correlations
120(2)
7.4.3 Subtests and reliability
122(1)
7.4.4 Estimating the magnitude of response dependence
122(1)
7.4.5 Illustration
122(5)
7.5 Summary
127(1)
7.6 Bibliography
128(3)
Chapter 8 Two Tests of Local Independence
131(6)
Svend Kreiner
Karl Bang Christensen
8.1 Introduction
131(1)
8.2 Kelderman's conditional likelihood ratio test of local independence
132(1)
8.3 Simple conditional independence tests
133(2)
8.4 Discussion and recommendations
135(1)
8.5 Bibliography
136(1)
Chapter 9 Dimensionality
137(22)
Mike Horton
Ida Marais
Karl Bang Christensen
9.1 Introduction
137(4)
9.1.1 Background
138(1)
9.1.2 Multidimensionality in health outcome scales
139(1)
9.1.3 Consequences of multidimensionality
140(1)
9.1.4 Motivating example: the HADS data
140(1)
9.2 Multidimensional models
141(1)
9.2.1 Marginal likelihood function
142(1)
9.2.2 Conditional likelihood function
142(1)
9.3 Diagnostics for detection of multidimensionality
142(7)
9.3.1 Analysis of residuals
143(1)
9.3.2 Observed and expected counts
143(2)
9.3.3 Observed and expected correlations
145(1)
9.3.4 The t-test approach
146(1)
9.3.5 Using reliability estimates as diagnostics of multidimensionality
147(2)
9.4 Tests of unidimensionality
149(3)
9.4.1 Tests based on diagnostics
149(1)
9.4.2 Likelihood tests
149(3)
9.5 Estimating the magnitude of multidimensionality
152(1)
9.6 Implementation
152(1)
9.7 Summary
152(2)
9.8 Bibliography
154(5)
Part 4 APPLYING THE RASCH MODEL
159(118)
Chapter 10 The Polytomous Rasch Model and the Equating of Two Instruments
163(34)
David Andrich
10.1 Introduction
163(2)
10.2 The Polytomous Rasch Model
165(6)
10.2.1 Conditional probabilities
165(2)
10.2.2 Conditional estimates of the instrument parameters
167(2)
10.2.3 An illustrative small example
169(2)
10.3 Reparameterization of the thresholds
171(6)
10.3.1 Thresholds reparameterized to two parameters for each instrument
171(4)
10.3.2 Thresholds reparameterized with more than two parameters
175(1)
10.3.3 A reparameterization with four parameters
175(1)
10.3.3.1 A solution algorithm
176(1)
10.3.3.2 Leunbach's precedent
176(1)
10.4 Tests of fit
177(4)
10.4.1 The conditional test of fit based on cell frequencies
177(1)
10.4.1.1 Degrees of freedom for the conditional test of fit based on cell frequencies
178(1)
10.4.2 The conditional test of fit based on class intervals
178(1)
10.4.2.1 Degrees of freedom for the conditional test of fit based on class intervals
179(1)
10.4.3 Graphical test of fit based on total scores
180(1)
10.4.4 Graphical test of fit based on person estimates
180(1)
10.5 Equating procedures
181(1)
10.5.1 Equating using conditioning on total scores
181(1)
10.5.2 Equating through person estimates
181(1)
10.6 Example
182(11)
10.6.1 Person threshold distribution
183(1)
10.6.2 The test of fit between the data and the model
183(1)
10.6.2.1 Conditional x2 test of fit based on cells of the data matrix and four moments estimated
183(1)
10.6.2.2 Conditional x2 test of fit based on class intervals of the data matrix and four moments estimated
184(1)
10.6.2.3 Conditional x2 test of fit based on cells of the data matrix and two moments estimated
185(1)
10.6.2.4 Conditional x2 test of fit based on class intervals of the data matrix and two moments estimated
185(1)
10.6.3 Further analysis with the parameterization with two moments for each instrument
186(1)
10.6.3.1 Parameter estimates from two moments
186(1)
10.6.3.2 Score characteristic curves
186(1)
10.6.3.3 Observed and expected frequencies in class intervals
186(1)
10.6.3.4 Graphical test of fit based on conditioning on total scores
186(1)
10.6.3.5 Graphical test of fit based on person estimates
187(1)
10.6.4 Equated scores based on the parameterization with two moments of the thresholds
188(1)
10.6.4.1 Equated scores conditional on the total score
189(1)
10.6.4.2 Equated scores given the person estimate
190(3)
10.7 Discussion
193(2)
10.8 Bibliography
195(2)
Chapter 11 A Multidimensional Latent Class Rasch Model for the Assessment of the Health-Related Quality of Life
197(22)
Silvia Bacci
Francesco Bartolucci
11.1 Introduction
197(3)
11.2 The data set
200(2)
11.3 The multidimensional latent class Rasch model
202(7)
11.3.1 Model assumptions
202(3)
11.3.2 Maximum likelihood estimation and model selection
205(2)
11.3.3 Software details
207(1)
11.3.4 Concluding remarks about the model
208(1)
11.4 Correlation between latent traits
209(3)
11.5 Application results
212(3)
11.6 Acknowledgments
215(1)
11.7 Bibliography
216(3)
Chapter 12 Analysis of Rater Agreement by Rasch and IRT Models
219(16)
Jørgen Holm Petersen
12.1 Introduction
219(1)
12.2 An IRT model for modeling inter-rater agreement
220(1)
12.3 Umbilical artery Doppler velocimetry and perinatal mortality
221(1)
12.4 Quantifying the rater agreement in the Rasch model
222(5)
12.4.1 Fixed-effects approach
222(3)
12.4.2 Random Effects approach and the median odds ratio
225(2)
12.5 Doppler velocimetry and perinatal mortality
227(2)
12.6 Quantifying the rater agreement in the IRT model
229(2)
12.7 Discussion
231(1)
12.8 Bibliography
232(3)
Chapter 13 From Measurement to Analysis
235(22)
Mounir Mesbah
13.1 Introduction
235(2)
13.2 Likelihood
237(1)
13.2.1 Two-step model
238(1)
13.2.2 Latent regression model
238(1)
13.3 First step: measurement models
238(3)
13.4 Statistical validation of measurement instrument
241(4)
13.5 Construction of scores
245(1)
13.6 Two-step method to analyze change between groups
246(4)
13.6.1 Health-related quality of life and housing in europe
246(2)
13.6.2 Use of surrogate in an clinical oncology trial
248(2)
13.7 Latent regression to analyze change between groups
250(3)
13.8 Conclusion
253(1)
13.9 Bibliography
254(3)
Chapter 14 Analysis with Repeatedly Measured Binary Item Response Data by Ad Hoc Rasch Scales
257(20)
Volkert Siersma
Paolo Eusebi
14.1 Introduction
257(3)
14.2 The generalized multilevel Rasch model
260(4)
14.2.1 The multilevel form of the conventional Rasch model for binary items
260(2)
14.2.2 Group comparison and repeated measurement
262(1)
14.2.3 Differential item functioning and local dependence
263(1)
14.3 The analysis of an ad hoc scale
264(4)
14.4 Simulation study
268(4)
14.5 Discussion
272(3)
14.6 Bibliography
275(2)
Part 5 CREATING, TRANSLATING AND IMPROVING RASCH SCALES
277(58)
Chapter 15 Writing Health-Related Items for Rasch Models - Patient-Reported Outcome Scales for Health Sciences: From Medical Paternalism to Patient Autonomy
281(22)
John Brodersen
Lynda C. Doward
Hanne Thorsen
Stephen P. McKenna
15.1 Introduction
281(3)
15.1.1 The emergence of the biopsychosocial model of illness
282(1)
15.1.2 Changes in the consultation process in general medicine
283(1)
15.2 The use of patient-reported outcome questionnaires
284(10)
15.2.1 Defining PRO constructs
285(1)
15.2.1.1 Measures of impairment, activity limitations and participation restrictions
285(2)
15.2.1.2 Health status/health-related quality of life
287(1)
15.2.1.3 Generic and specific questionnaires
288(2)
15.2.2 Quality requirements for PRO questionnaires
290(1)
15.2.2.1 Instrument development standards
290(1)
15.2.2.2 Psychometric and scaling standards
291(3)
15.3 Writing new health-related items for new PRO scales
294(3)
15.3.1 Consideration of measurement issues
294(1)
15.3.2 Questionnaire development
294(3)
15.4 Selecting PROs for a clinical setting
297(1)
15.5 Conclusions
297(1)
15.6 Bibliography
298(5)
Chapter 16 Adapting Patient-Reported Outcome Measures for Use in New Languages and Cultures
303(14)
Stephen P. McKenna
Jeanette Wilburn
Hanne Thorsen
John Brodersen
16.1 Introduction
303(2)
16.1.1 Background
303(1)
16.1.2 Aim of the adaptation process
304(1)
16.2 Suitability for adaptation
305(1)
16.3 Translation process
305(1)
16.3.1 Linguistic issues
305(1)
16.3.2 Conceptual issues
306(1)
16.3.3 Technical issues
306(1)
16.4 Translation methodology
306(2)
16.4.1 Forward-backward translation
307(1)
16.4.1.1 Situation 1: The forward translation is good
307(1)
16.4.1.2 Situation 2: The forward translation is good, but the back translation is poor
308(1)
16.4.1.3 Situation 3: The forward translation is poor
308(1)
16.5 Dual-panel translation
308(2)
16.5.1 Bilingual panel
308(1)
16.5.2 Lay panel
309(1)
16.6 Assessment of psychometric and scaling properties
310(5)
16.6.1 Cognitive debriefing interviews
310(1)
16.6.1.1 Interview setting
311(1)
16.6.1.2 Materials
311(1)
16.6.1.3 Reporting on the interviews
311(1)
16.6.2 Determining the psychometric properties of the new language version of the measure
312(1)
16.6.3 Practice guidelines
313(2)
16.7 Bibliography
315(2)
Chapter 17 Improving Items That Do Not Fit the Rasch Model
317(18)
Tine Nielsen
Svend Kreiner
17.1 Introduction
317(1)
17.2 The RM and the graphical log-linear RM
318(2)
17.3 The scale improvement strategy
320(6)
17.3.1 Choice of modification action
322(3)
17.3.2 Result of applying the scale improvement strategy
325(1)
17.4 Application of the strategy to the Physical Functioning Scale of the SF-36
326(5)
17.4.1 Results of the GLLRM
326(1)
17.4.2 Results of the subject matter analysis
327(1)
17.4.3 Suggestions according to the strategy
328(3)
17.5 Closing remark
331(1)
17.6 Bibliography
331(4)
Part 6 ANALYZING AND REPORTING RASCH MODELS
335(28)
Chapter 18 Software for Rasch Analysis
337(10)
Mounir Mesbah
18.1 Introduction
337(1)
18.2 Stand alone softwares packages
338(1)
18.2.1 WINSTEPS
338(1)
18.2.2 RUMM
338(1)
18.2.3 CONQUEST
338(1)
18.2.4 DIGRAM
339(1)
18.3 Implementations in standard software
339(1)
18.3.1 SAS macro for MML estimation
339(1)
18.3.2 SAS macros based on CML estimation
340(1)
18.3.3 eRm: an R Package
340(1)
18.4 Fitting the Rasch model in SAS
340(4)
18.4.1 Simulation of Rasch dichotomous items
340(1)
18.4.2 MML estimation using PROC NLMIXED
341(1)
18.4.3 MML estimation of using PROC GLIMMIX
342(1)
18.4.4 JML estimation using PROC LOGISTIC
342(1)
18.4.5 CML estimation using PROC GENMOD
343(1)
18.4.6 JML estimation using PROC LOGISTIC
343(1)
18.4.7 Results
344(1)
18.5 Bibliography
344(3)
Chapter 19 Reporting a Rasch Analysis
347(16)
Thomas Salzberger
19.1 Introduction
347(3)
19.1.1 Objectives
347(1)
19.1.2 Factors impacting a Rasch analysis report
348(1)
19.1.3 The role of the substantive theory of the latent variable
349(1)
19.1.4 The frame of reference
350(1)
19.2 Suggested elements
350(10)
19.2.1 Construct: definition and operationalization of the latent variable
351(1)
19.2.2 Response format and scoring
351(1)
19.2.3 Sample and sampling design
352(1)
19.2.4 Data
353(1)
19.2.5 Measurement model and technical aspects
353(1)
19.2.6 Fit analysis
354(1)
19.2.7 Response scale suitability
355(1)
19.2.8 Item fit assessment
355(1)
19.2.9 Person fit assessment
356(1)
19.2.10 Information
357(1)
19.2.11 Validated scale
357(1)
19.2.12 Application and usefulness
358(1)
19.2.13 Further issues
359(1)
19.3 Bibliography
360(3)
List of Authors 363(2)
Index 365
Karl Bang Christensen is Associate Professor at the Department of Biostatistics at the University of Copenhagen in Denmark. With a background in mathematical statistics he has worked mainly within Biostatistics and Epidemiology. Inspired by the issue of measurement in social and health sciences he has published methodological work about Rasch models in journals such as Applied Psychological Measurement, the British Journal of Mathematical and Statistical Psychology and Psychometrika.

Svend Kreiner is Professor at the Deptartment of Biostatistics, Institute of Public Health, University of Copenhagen, Denmark. He has for some years tried to combine his interest in Rasch models with his interest in graphical models for categorical data and has developed a family of Rasch-related models that he refers to as graphical loglinear Rasch models in which several of the problems with Rasch models for social and health science data have been resolved.

Mounir Mesbah is Professor of Statistics at the Department of Mathematics and Statistics, University Pierre and Marie Curie, Paris, France. Within the Department of Mathematics and Statistics, he is currently teaching at the ISUP (UPMC Institute of Statistics) and is in charge of biostatistical options.
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