Details
Rasch Models in Health
1. Aufl.
144,99 € |
|
Verlag: | Wiley |
Format: | |
Veröffentl.: | 24.01.2013 |
ISBN/EAN: | 9781118574447 |
Sprache: | englisch |
Anzahl Seiten: | 384 |
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Beschreibungen
<p>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.</p> <p>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.</p>
<p>I Probabilistic models 1</p> <p>1 The Rasch model for dichotomous items 3</p> <p>1.1 Introduction 4</p> <p>1.1.1 original formulation of the model 4</p> <p>1.1.2 Modern formulations of the model 7</p> <p>1.2 Psychometric properties 8</p> <p>1.2.1 Requirements of IRT models 9</p> <p>1.2.2 Item Characteristic Curves 10</p> <p>1.2.3 Guttman errors 10</p> <p>1.2.4 Implicit assumptions 11</p> <p>1.3 Statistical properties 11</p> <p>1.3.1 The distribution of the total score 12</p> <p>1.3.2 Symmetrical polynomials 13</p> <p>1.3.3 Test characteristic curve (TCC) 14</p> <p>1.3.4 Partial credit model parametrization of the score distribution 14</p> <p>1.3.5 Rasch models for subscores 15</p> <p>1.4 Inference frames 15</p> <p>1.5 Specic objectivity 18</p> <p>1.6 Rasch models as graphical models 19</p> <p>1.7 Summary 20</p> <p>2 Rasch models for ordered polytomous items 25</p> <p>2.1 Introduction 26</p> <p>2.1.1 Example 26</p> <p>2.1.2 Ordered categories 26</p> <p>2.1.3 Properties of the Polytomous Rasch model 30</p> <p>2.1.4 Assumptions 32</p> <p>2.2 Derivation from the dichotomous model 32</p> <p>2.3 Distributions derived from Rasch models 37</p> <p>2.3.1 The score distribution 37</p> <p>2.3.2 Interpretation of thresholds in partial credit items and Rasch</p> <p>scores 39</p> <p>2.3.3 Conditional distribution of item responses given the total score 39</p> <p>2.4 Conclusion 39</p> <p>2.4.1 Frames of inference for Rasch models 40</p> <p>II Inference in the Rasch model 45</p> <p>3 Estimation of item parameters 47</p> <p>3.1 Introduction 48</p> <p>3.2 Estimation of item parameters 50</p> <p>3.2.1 Estimation using the conditional likelihood function 50</p> <p>3.2.2 Pairwise conditional estimation 52</p> <p>3.2.3 Marginal likelihood function 54</p> <p>3.2.4 Extended likelihood function 55</p> <p>3.2.5 Reduced rank parametrization 56</p> <p>3.2.6 Parameter estimation in more general Rasch models 56</p> <p>4 Person parameter estimation and measurement in Rasch models 59</p> <p>4.1 Introduction and notation 60</p> <p>4.2 Maximum likelihood estimation of person parameters 61</p> <p>4.3 Item and test information functions 62</p> <p>4.4 Weighted likelihood estimation of person parameters 63</p> <p>4.5 Example 63</p> <p>4.6 Measurement quality 65</p> <p>4.6.1 Reliability in classical test theory 66</p> <p>4.6.2 Reliability in Rasch models 67</p> <p>4.6.3 Expected measurement precision 69</p> <p>4.6.4 Targeting 69</p> <p>III Checking the Rasch model 75</p> <p>5 Itemt statistics 77</p> <p>5.1 Introduction 78</p> <p>5.2 Rasch model residuals 79</p> <p>5.2.1 Notation 79</p> <p>5.2.2 Individual response residuals: outts and ints 80</p> <p>5.2.3 Group residuals 85</p> <p>5.2.4 Group residuals for analysis of homogeneity 85</p> <p>5.3 Molenaar's U 87</p> <p>5.4 Analysis of item { restscore association 88</p> <p>5.5 Group residuals and analysis of DIF 89</p> <p>5.6 Kelderman's conditional likelihood ratio test of no DIF 90</p> <p>5.7 Test for conditional independence in three-way tables 92</p> <p>5.8 Discussion and recommendations 93</p> <p>5.8.1 Technical issues 93</p> <p>5.8.2 What to do when items do not agree with the Rasch model 95</p> <p>6 Over-all tests of the Rasch model 99</p> <p>6.1 Introduction 100</p> <p>6.2 The conditional likelihood ratio test 100</p> <p>6.3 Example: Diabetes and Eating habits 102</p> <p>6.4 Other over-all tests of t 104</p> <p>7 Local dependence 107</p> <p>7.1 Introduction 108</p> <p>7.1.1 Reduced rank parametrization model for sub tests 108</p> <p>7.1.2 Reliability indexes 109</p> <p>7.2 Local dependence in Rasch Models 109</p> <p>7.2.1 Response dependence 110</p> <p>7.3 E</p> <p>ects of response dependence on measurement 111</p> <p>7.4 Diagnosing and detecting response dependence 114</p> <p>7.4.1 Item t 114</p> <p>7.4.2 Item residual correlations 116</p> <p>7.4.3 Sub tests and reliability 118</p> <p>7.4.4 Estimating the magnitude of response dependence 118</p> <p>7.4.5 Illustration 119</p> <p>7.5 Summary 124</p> <p>8 Two tests of local independence 131</p> <p>8.1 Introduction 132</p> <p>8.2 Kelderman's conditional likelihood ratio test of local independence 132</p> <p>8.3 Simple conditional independence tests 134</p> <p>8.4 Discussion and recommendations 136</p> <p>9 Dimensionality 139</p> <p>9.1 Introduction 140</p> <p>9.1.1 Background 140</p> <p>9.1.2 Multidimensionality in health outcome scales 141</p> <p>9.1.3 Consequences of multidimensionality 142</p> <p>9.1.4 Motivating example: the HADS data 142</p> <p>9.2 Multidimensional models 143</p> <p>9.2.1 Marginal likelihood function 144</p> <p>9.2.2 Conditional likelihood function 144</p> <p>9.3 Diagnostics for detection of multidimensionality 144</p> <p>9.3.1 Analysis of residuals 145</p> <p>9.3.2 Observed and expected counts 145</p> <p>9.3.3 Observed and expected correlations 147</p> <p>9.3.4 The t-test approach 148</p> <p>9.3.5 Using reliability estimates as diagnostics of multidimensionality 149</p> <p>9.3.6 Tests of unidimensionality 150</p> <p>9.4 Estimating the magnitude of multidimensionality 152</p> <p>9.5 Implementation 153</p> <p>9.6 Summary 153</p> <p>IV Applying the Rasch model 161</p> <p>10 The polytomous Rasch model and the equating of two instruments163</p> <p>10.1 Introduction 164</p> <p>10.2 The polytomous Rasch model 165</p> <p>10.2.1 Conditional probabilities 166</p> <p>10.2.2 Conditional estimates of the instrument parameters 167</p> <p>10.2.3 An illustrative small example 169</p> <p>10.3 Reparametrization of the thresholds 170</p> <p>10.3.1 Thresholds reparametrized to two parameters for each instrument170</p> <p>10.3.2 Thresholds reparametrized with more than two parameters 174</p> <p>10.3.3 A reparametrization with four parameters 174</p> <p>10.4 Tests of Fit 176</p> <p>10.4.1 The conditional test of fit based on cell frequencies 176</p> <p>10.4.2 The conditional test of fit based on class intervals 177</p> <p>10.4.3 Graphical test of fit based on total scores 178</p> <p>10.4.4 Graphical test of fit based on person estimates 179</p> <p>10.5 Equating procedures 179</p> <p>10.5.1 Equating using conditioning on total scores 180</p> <p>10.5.2 Equating through person estimates 180</p> <p>10.6 Example 180</p> <p>10.6.1 Person threshold distribution 182</p> <p>10.6.2 The test of </p> <p>t between the data and the model 182</p> <p>10.6.3 Further analysis with the parametrization with two moments</p> <p>for each instrument 184</p> <p>10.6.4 Equated scores based on the parametrization with two moments</p> <p>of the thresholds 190</p> <p>10.7 Discussion 194</p> <p>11 A multidimensional latent class Rasch model for the assessment of</p> <p>the Health-related Quality of Life 199</p> <p>11.1 Introduction 200</p> <p>11.2 The dataset 202</p> <p>11.3 The multidimensional latent class Rasch model 205</p> <p>11.3.1 Model assumptions 205</p> <p>11.3.2 Maximum likelihood estimation and model selection 208</p> <p>11.3.3 Software details 209</p> <p>11.3.4 Concluding remarks about the model 210</p> <p>11.4 Inference on the correlation between latent traits 211</p> <p>11.5 Application results 214</p> <p>12 Analysis of Rater Agreement by Rasch and IRT models 223</p> <p>12.1 Introduction 224</p> <p>12.2 An IRT model for modelling inter-rater agreement 224</p> <p>12.3 Umbilical artery Doppler velocimetry and perinatal mortality 226</p> <p>12.4 Quantifying the rater agreement in the Rasch model 227</p> <p>12.4.1 Fixed Effects Approach 227</p> <p>12.4.2 Random Effects approach and the median odds ratio 229</p> <p>12.5 Doppler velocimetry and perinatal mortality 231</p> <p>12.6 Quantifying the rater agreement in the IRT model 232</p> <p>12.7 Discussion 233</p> <p>13 From Measurement to Analysis: two steps or latent regression? 241</p> <p>13.1 Introduction 242</p> <p>13.2 Likelihood 243</p> <p>13.2.1 Two-step model 244</p> <p>13.2.2 Latent regression model 244</p> <p>13.3 First step: Measurement models 245</p> <p>13.4 Statistical Validation of Measurement Instrument 248</p> <p>13.5 Construction of Scores 251</p> <p>13.6 Two-step method to Analyze Change between Groups 253</p> <p>13.6.1 Health related Quality of Life and Housing in Europe 253</p> <p>13.6.2 Use of Surrogate in an Clinical Oncology trial 254</p> <p>13.7 Latent Regression to Analyze Change between Groups 257</p> <p>13.8 Conclusion 259</p> <p>14 Analysis with repeatedly measured binary item response data byad</p> <p>hoc Rasch scales 265</p> <p>14.1 Introduction 266</p> <p>14.2 The generalized multilevel Rasch model 268</p> <p>14.2.1 The multilevel form of the conventional Rasch model for binary</p> <p>items 268</p> <p>14.2.2 Group comparison and repeated measurement 269</p> <p>14.2.3 Differential item functioning and local dependence 270</p> <p>14.3 The analysis of an ad hoc scale 272</p> <p>14.4 Simulation study 277</p> <p>14.5 Discussion 283</p> <p>V Creating, translating, improving Rasch scales 287</p> <p>15 Writing Health-Related Items for Rasch Models - Patient Reported</p> <p>Outcome Scales for Health Sciences: From Medical Paternalism to</p> <p>Patient Autonomy 289</p> <p>15.1 Introduction 290</p> <p>15.1.1 The emergence of the biopsychosocial model of illness 290</p> <p>15.1.2 Changes in the consultation process in general medicine 291</p> <p>15.2 The use of patient reported outcome questionnaires 292</p> <p>15.2.1 Defining PRO constructs 293</p> <p>15.2.2 Quality requirements for PRO questionnaires 298</p> <p>15.3 Writing new Health-Related Items for new PRO scales 301</p> <p>15.3.1 Consideration of measurement issues 302</p> <p>15.3.2 Questionnaire Development 302</p> <p>15.4 Selecting PROs for a clinical setting 305</p> <p>15.5 Conclusions 305</p> <p>16 Adapting patient-reported outcome measures for use in new lan-</p> <p>guages and cultures 313</p> <p>16.1 Introduction 314</p> <p>16.1.1 Background 314</p> <p>16.1.2 Aim of the adaptation process 315</p> <p>16.2 Suitability for adaptation 315</p> <p>16.3 Translation Process 315</p> <p>16.3.1 Linguistic Issues 316</p> <p>16.3.2 Conceptual Issues 316</p> <p>16.3.3 Technical Issues 316</p> <p>16.4 Translation Methodology 317</p> <p>16.4.1 Forward-backward translation 317</p> <p>16.5 Dual-Panel translation 318</p> <p>16.6 Assessment of psychometric and scaling properties 320</p> <p>16.6.1 Cognitive debriefing interviews 320</p> <p>16.6.2 Determining the psychometric properties of the new language</p> <p>version of the measure 322</p> <p>16.6.3 Practice Guidelines 323</p> <p>17 Improving items that do not fit the Rasch model 329</p> <p>17.1 Introduction 330</p> <p>17.2 The Rasch model and the graphical log linear Rasch model 330</p> <p>17.3 The scale improvement strategy 332</p> <p>17.3.1 Choice of modificational action 335</p> <p>17.3.2 Result of applying the scale improvement strategy 339</p> <p>17.4 Application of the strategy to the Physical Functioning Scale of the</p> <p>SF-36 340</p> <p>17.4.1 Results of the GLLRM 340</p> <p>17.4.2 Results of the subject matter analysis 341</p> <p>17.4.3 Suggestions according to the strategy 342</p> <p>17.5 Closing remark 345</p> <p>VI Analyzing and reporting Rasch models 349</p> <p>18 Software and program for Rasch Analysis 351</p> <p>18.1 Introduction 352</p> <p>18.2 Stand alone softwares packages 352</p> <p>18.2.1 WINSTEPS 352</p> <p>18.2.2 RUMM 353</p> <p>18.2.3 Conquest 353</p> <p>18.2.4 DIGRAM 354</p> <p>18.3 Implementations in standard software 355</p> <p>18.3.1 SAS macro for MML estimation: %ANAQOL 355</p> <p>18.3.2 SAS Macros based on CML 356</p> <p>18.3.3 eRm : an R Package 356</p> <p>18.4 Fitting the Rasch model in SAS 356</p> <p>18.4.1 Simulation of Rasch dichotomous items 356</p> <p>18.4.2 MML Estimation of Rasch parameters using Proc NLMIXED 357</p> <p>18.4.3 MML Estimation of Rasch parameters using Proc GLIMMIX 358</p> <p>18.4.4 CML Estimation of Rasch parameters using Proc GENMOD 358</p> <p>18.4.5 JML Estimation of Rasch parameters using Proc LOGISTIC 359</p> <p>18.4.6 Loglinear Rasch model Estimation of Rasch parameters using</p> <p>Proc Logistic 360</p> <p>18.4.7 Results 360</p> <p>19 Reporting a Rasch analysis 363</p> <p>19.1 Introduction 364</p> <p>19.1.1 Objectives 364</p> <p>19.1.2 Factors impacting a Rasch analysis report 364</p> <p>19.1.3 The role of the substantive theory of the latent variable 366</p> <p>19.1.4 The frame of reference 367</p> <p>19.2 Suggested Elements 367</p> <p>19.2.1 Construct: definition and operationalisation of the latent variable367</p> <p>19.2.2 Response format and scoring 368</p> <p>19.2.3 Sample and sampling design 368</p> <p>19.2.4 Data 369</p> <p>19.2.5 Measurement model and technical aspects 370</p> <p>19.2.6 Fit analysis 370</p> <p>19.2.7 Response scale suitability 371</p> <p>19.2.8 Item fit assessment 372</p> <p>19.2.9 Person fit assessment 372</p> <p>19.2.10 Information 373</p> <p>19.2.11Validated scale 374</p> <p>19.2.12 Application and usefulness 375</p> <p>19.2.13Further issues 376</p>
<p>"This book contains a comprehensive overview of the statistical theory of Rasch models." (<i>Zentralblatt MATH</i> 2016)</p>
<p><b>Karl Bang Christensen</b> 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.</p><p><b> Svend Kreiner</b> 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. </p><p><b>Mounir Mesbah</b> 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. </p>
<p>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. </p><p> 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. </p>