Rasch Models in Health

Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 21882119

List of contents

I Probabilistic models 1
1 The Rasch model for dichotomous items 3
1.1 Introduction 4
1.1.1 original formulation of the model  4
1.1.2 Modern formulations of the model  7
1.2 Psychometric properties 8
1.2.1 Requirements of IRT models 9
1.2.2 Item Characteristic Curves 10
1.2.3 Guttman errors 10
1.2.4 Implicit assumptions  11
1.3 Statistical properties 11
1.3.1 The distribution of the total score  12
1.3.2 Symmetrical polynomials 13
1.3.3 Test characteristic curve (TCC)  14
1.3.4 Partial credit model parametrization of the score distribution 14
1.3.5 Rasch models for subscores 15
1.4 Inference frames  15
1.5 Specic objectivity 18
1.6 Rasch models as graphical models 19
1.7 Summary 20
2 Rasch models for ordered polytomous items 25
2.1 Introduction 26
2.1.1 Example  26
2.1.2 Ordered categories  26
2.1.3 Properties of the Polytomous Rasch model   30
2.1.4 Assumptions 32
2.2 Derivation from the dichotomous model  32
2.3 Distributions derived from Rasch models  37
2.3.1 The score distribution  37
2.3.2 Interpretation of thresholds in partial credit items and Rasch
scores  39
2.3.3 Conditional distribution of item responses given the total score 39
2.4 Conclusion 39
2.4.1 Frames of inference for Rasch models    40
II Inference in the Rasch model 45
3 Estimation of item parameters 47
3.1 Introduction 48
3.2 Estimation of item parameters  50
3.2.1 Estimation using the conditional likelihood function  50
3.2.2 Pairwise conditional estimation  52
3.2.3 Marginal likelihood function 54
3.2.4 Extended likelihood function 55
3.2.5 Reduced rank parametrization 56
3.2.6 Parameter estimation in more general Rasch models  56
4 Person parameter estimation and measurement in Rasch models 59
4.1 Introduction and notation  60
4.2 Maximum likelihood estimation of person parameters   61
4.3 Item and test information functions 62
4.4 Weighted likelihood estimation of person parameters   63
4.5 Example 63
4.6 Measurement quality 65
4.6.1 Reliability in classical test theory  66
4.6.2 Reliability in Rasch models 67
4.6.3 Expected measurement precision  69
4.6.4 Targeting  69
III Checking the Rasch model 75
5 Itemt statistics 77
5.1 Introduction 78
5.2 Rasch model residuals 79
5.2.1 Notation  79
5.2.2 Individual response residuals: outts and ints   80
5.2.3 Group residuals 85
5.2.4 Group residuals for analysis of homogeneity   85
5.3 Molenaar's U  87
5.4 Analysis of item { restscore association  88
5.5 Group residuals and analysis of DIF 89
5.6 Kelderman's conditional likelihood ratio test of no DIF   90
5.7 Test for conditional independence in three-way tables   92
5.8 Discussion and recommendations 93
5.8.1 Technical issues 93
5.8.2 What to do when items do not agree with the Rasch model 95
6 Over-all tests of the Rasch model 99
6.1 Introduction 100
6.2 The conditional likelihood ratio test 100
6.3 Example: Diabetes and Eating habits 102
6.4 Other over-all tests of t 104
7 Local dependence 107
7.1 Introduction 108
7.1.1 Reduced rank parametrization model for sub tests  108
7.1.2 Reliability indexes  109
7.2 Local dependence in Rasch Models 109
7.2.1 Response dependence  110
7.3 E
ects of response dependence on measurement    111
7.4 Diagnosing and detecting response dependence    114
7.4.1 Item t  114
7.4.2 Item residual correlations 116
7.4.3 Sub tests and reliability 118
7.4.4 Estimating the magnitude of response dependence  118
7.4.5 Illustration 119
7.5 Summary 124
8 Two tests of local independence 131
8.1 Introduction 132
8.2 Kelderman's conditional likelihood ratio test of local independence 132
8.3 Simple conditional independence tests 134
8.4 Discussion and recommendations 136
9 Dimensionality 139
9.1 Introduction 140
9.1.1 Background 140
9.1.2 Multidimensionality in health outcome scales   141
9.1.3 Consequences of multidimensionality    142
9.1.4 Motivating example: the HADS data    142
9.2 Multidimensional models 143
9.2.1 Marginal likelihood function 144
9.2.2 Conditional likelihood function  144
9.3 Diagnostics for detection of multidimensionality    144
9.3.1 Analysis of residuals  145
9.3.2 Observed and expected counts 145
9.3.3 Observed and expected correlations    147
9.3.4 The t-test approach  148
9.3.5 Using reliability estimates as diagnostics of multidimensionality 149
9.3.6 Tests of unidimensionality 150
9.4 Estimating the magnitude of multidimensionality   152
9.5 Implementation  153
9.6 Summary 153
IV Applying the Rasch model 161
10 The polytomous Rasch model and the equating of two instruments163
10.1 Introduction 164
10.2 The polytomous Rasch model  165
10.2.1 Conditional probabilities 166
10.2.2 Conditional estimates of the instrument parameters  167
10.2.3 An illustrative small example 169
10.3 Reparametrization of the thresholds 170
10.3.1 Thresholds reparametrized to two parameters for each instrument170
10.3.2 Thresholds reparametrized with more than two parameters 174
10.3.3 A reparametrization with four parameters   174
10.4 Tests of Fit 176
10.4.1 The conditional test of fit based on cell frequencies  176
10.4.2 The conditional test of fit based on class intervals  177
10.4.3 Graphical test of fit based on total scores    178
10.4.4 Graphical test of fit based on person estimates   179
10.5 Equating procedures 179
10.5.1 Equating using conditioning on total scores   180
10.5.2 Equating through person estimates    180
10.6 Example 180
10.6.1 Person threshold distribution 182
10.6.2 The test of 
t between the data and the model   182
10.6.3 Further analysis with the parametrization with two moments
for each instrument  184
10.6.4 Equated scores based on the parametrization with two moments
of the thresholds 190
10.7 Discussion 194
11 A multidimensional latent class Rasch model for the assessment of
the Health-related Quality of Life 199
11.1 Introduction 200
11.2 The dataset 202
11.3 The multidimensional latent class Rasch model    205
11.3.1 Model assumptions  205
11.3.2 Maximum likelihood estimation and model selection  208
11.3.3 Software details 209
11.3.4 Concluding remarks about the model    210
11.4 Inference on the correlation between latent traits   211
11.5 Application results 214
12 Analysis of Rater Agreement by Rasch and IRT models 223
12.1 Introduction 224
12.2 An IRT model for modelling inter-rater agreement   224
12.3 Umbilical artery Doppler velocimetry and perinatal mortality  226
12.4 Quantifying the rater agreement in the Rasch model   227
12.4.1 Fixed Effects Approach  227
12.4.2 Random Effects approach and the median odds ratio  229
12.5 Doppler velocimetry and perinatal mortality    231
12.6 Quantifying the rater agreement in the IRT model   232
12.7 Discussion 233
13 From Measurement to Analysis: two steps or latent regression? 241
13.1 Introduction 242
13.2 Likelihood 243
13.2.1 Two-step model 244
13.2.2 Latent regression model 244
13.3 First step: Measurement models 245
13.4 Statistical Validation of Measurement Instrument   248
13.5 Construction of Scores 251
13.6 Two-step method to Analyze Change between Groups   253
13.6.1 Health related Quality of Life and Housing in Europe  253
13.6.2 Use of Surrogate in an Clinical Oncology trial   254
13.7 Latent Regression to Analyze Change between Groups   257
13.8 Conclusion 259
14 Analysis with repeatedly measured binary item response data byad
hoc Rasch scales 265
14.1 Introduction 266
14.2 The generalized multilevel Rasch model  268
14.2.1 The multilevel form of the conventional Rasch model for binary
items 268
14.2.2 Group comparison and repeated measurement   269
14.2.3 Differential item functioning and local dependence  270
14.3 The analysis of an ad hoc scale 272
14.4 Simulation study  277
14.5 Discussion 283
V Creating, translating, improving Rasch scales 287
15 Writing Health-Related Items for Rasch Models - Patient Reported
Outcome Scales for Health Sciences: From Medical Paternalism to
Patient Autonomy 289
15.1 Introduction 290
15.1.1 The emergence of the biopsychosocial model of illness  290
15.1.2 Changes in the consultation process in general medicine  291
15.2 The use of patient reported outcome questionnaires   292
15.2.1 Defining PRO constructs 293
15.2.2 Quality requirements for PRO questionnaires   298
15.3 Writing new Health-Related Items for new PRO scales   301
15.3.1 Consideration of measurement issues    302
15.3.2 Questionnaire Development 302
15.4 Selecting PROs for a clinical setting 305
15.5 Conclusions 305
16 Adapting patient-reported outcome measures for use in new lan-
guages and cultures 313
16.1 Introduction 314
16.1.1 Background 314
16.1.2 Aim of the adaptation process 315
16.2 Suitability for adaptation 315
16.3 Translation Process 315
16.3.1 Linguistic Issues 316
16.3.2 Conceptual Issues 316
16.3.3 Technical Issues 316
16.4 Translation Methodology 317
16.4.1 Forward-backward translation 317
16.5 Dual-Panel translation 318
16.6 Assessment of psychometric and scaling properties   320
16.6.1 Cognitive debriefing interviews  320
16.6.2 Determining the psychometric properties of the new language
version of the measure  322
16.6.3 Practice Guidelines  323
17 Improving items that do not fit the Rasch model 329
17.1 Introduction 330
17.2 The Rasch model and the graphical log linear Rasch model  330
17.3 The scale improvement strategy 332
17.3.1 Choice of modificational action  335
17.3.2 Result of applying the scale improvement strategy  339
17.4 Application of the strategy to the Physical Functioning Scale of the
SF-36 340
17.4.1 Results of the GLLRM  340
17.4.2 Results of the subject matter analysis    341
17.4.3 Suggestions according to the strategy    342
17.5 Closing remark  345
VI Analyzing and reporting Rasch models 349
18 Software and program for Rasch Analysis 351
18.1 Introduction 352
18.2 Stand alone softwares packages 352
18.2.1 WINSTEPS 352
18.2.2 RUMM  353
18.2.3 Conquest  353
18.2.4 DIGRAM  354
18.3 Implementations in standard software 355
18.3.1 SAS macro for MML estimation: %ANAQOL   355
18.3.2 SAS Macros based on CML 356
18.3.3 eRm : an R Package  356
18.4 Fitting the Rasch model in SAS 356
18.4.1 Simulation of Rasch dichotomous items    356
18.4.2 MML Estimation of Rasch parameters using Proc NLMIXED 357
18.4.3 MML Estimation of Rasch parameters using Proc GLIMMIX 358
18.4.4 CML Estimation of Rasch parameters using Proc GENMOD 358
18.4.5 JML Estimation of Rasch parameters using Proc LOGISTIC 359
18.4.6 Loglinear Rasch model Estimation of Rasch parameters using
Proc Logistic 360
18.4.7 Results  360
19 Reporting a Rasch analysis 363
19.1 Introduction 364
19.1.1 Objectives  364
19.1.2 Factors impacting a Rasch analysis report   364
19.1.3 The role of the substantive theory of the latent variable  366
19.1.4 The frame of reference  367
19.2 Suggested Elements 367
19.2.1 Construct: definition and operationalisation of the latent variable367
19.2.2 Response format and scoring 368
19.2.3 Sample and sampling design 368
19.2.4 Data 369
19.2.5 Measurement model and technical aspects   370
19.2.6 Fit analysis 370
19.2.7 Response scale suitability 371
19.2.8 Item fit assessment  372
19.2.9 Person fit assessment  372
19.2.10 Information 373
19.2.11Validated scale 374
19.2.12 Application and usefulness 375
19.2.13Further issues 376

About the author

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.

Product details

• Authors: Karl Bang Christensen, Karl Bang (EDT)/ Kreiner Christensen, Svend Kreiner
• Assisted by: Karl Bang Christensen (Editor), Svend Kreiner (Editor), Mounir Mesbah (Editor)
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 26.12.2012
• EAN: 9781848212220
• ISBN: 978-1-84821-222-0
• Series: Applied Mathematics; Applied Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous