Rasch Models in Health

Rasch Modelsin Health......Page 2
Copyright
......Page 3
Table of Contents......Page 4
Preface......Page 14
PART 1 Probabilistic Models......Page 16
Introduction
......Page 17
1.1.1. Original formulation of the model......Page 18
1.1.2. Modern formulations of the model......Page 22
1.1.3. Psychometric properties......Page 23
1.1.3.1. Requirements of IRT models......Page 24
1.3. Guttman erro......Page 25
1.5. Implicit assumptions......Page 26
1.6. Statistical properties......Page 27
1.6.1. The distribution of the total score......Page 28
1.6.2. Symmetrical polynomials......Page 29
1.6.4. Rasch models for subscores......Page 30
1.7. Inference frames......Page 31
1.8. Specific objectivity......Page 33
1.9. Rasch models as graphical models......Page 34
1.10. Summary......Page 35
1.11. Bibliography......Page 37
2.1.1. Example......Page 39
2.1.2. Ordered categories......Page 40
2.1.3. Properties of the polytomous Rasch model......Page 43
2.2. Derivation from the dichotomous model......Page 45
2.3. Distributions derived from Rasch models......Page 49
2.3.1. The score distribution......Page 51
2.3.2. Conditional distribution of item responses given the total score......Page 52
2.4. Bibliography......Page 53
PART 2 Inference in the Rasch Model......Page 54
Introduction
......Page 55
3.1. Introduction......Page 58
3.2. Estimation of item parameters......Page 60
3.2.1. Estimation using the conditional likelihood function......Page 61
3.2.2. Pairwise conditional estimation......Page 63
3.2.3. Marginal likelihood function......Page 65
3.2.4. Extended likelihood function......Page 66
3.2.5. Reduced rank paramete......Page 67
3.3. Example......Page 68
3.4. Bibliography......Page 69
4.1. Introduction and notation......Page 71
4.2. Maximum likelihood estimation of person parameters......Page 73
4.3. Item and test information functions......Page 74
4.5. Example......Page 75
4.6.1. Reliability in classical test theory......Page 78
4.6.2. Reliability in Rasch models......Page 79
4.6.3. Expected measurement precision......Page 81
4.6.4. Targeting......Page 82
4.7. Bibliography......Page 84
PART 3 Checking the Rasch Model......Page 86
Introduction......Page 87
5.1. Introduction......Page 88
5.2.1. Notation......Page 89
5.2.2. Individual response residuals: outfits and infits......Page 91
5.2.3. Problem 1: the distribution of outfit and infit test statistics......Page 92
5.2.4. Problem 2: calculating Evi......Page 93
5.2.5. Group residuals......Page 95
5.2.6. Group residuals for analysis of homogeneity......Page 96
5.3. Molenaar’s U......Page 98
5.4. Analysis of item-restscore association......Page 99
5.6. Kelderman’s conditional likelihood ratio test of no DIF......Page 101
5.7. Test for conditional independence in three-way tables......Page 103
5.8.1. Technical issues......Page 105
5.8.2. What to do when items do not agree with the Rasch model......Page 106
5.9. Bibliography......Page 107
6.2. The conditional likelihood ratio test......Page 109
6.4. Bibliography......Page 113
7.1. Introduction......Page 114
7.1.2. Reliability indices......Page 115
7.2.1. Response dependence......Page 116
7.3. Effects of response dependence on measurement......Page 117
7.4.1. Item fit......Page 121
7.4.2. Item residual correlations......Page 123
7.4.5. Illustration......Page 125
7.5. Summary......Page 130
7.6. Bibliography......Page 131
8.1. Introduction......Page 134
8.2. Kelderman’s conditional likelihood ratio test of local independence......Page 135
8.3. Simple conditional independence tests......Page 136
8.4. Discussion and recommendations......Page 138
8.5. Bibliography......Page 139
9.1. Introduction......Page 140
9.1.1. Background......Page 141
9.1.2. Multidimensionality in health outcome scales......Page 142
9.1.4. Motivating example: the HADS data......Page 143
9.2. Multidimensional models......Page 144
9.3. Diagnostics for detection of multidimensionality......Page 145
9.3.2. Observed and expected counts......Page 146
9.3.3. Observed and expected correlations......Page 148
9.3.4. The t-test approach......Page 149
9.3.5. Using reliability estimates as diagnostics of multidimensionality......Page 150
9.4.2. Likelihood tests......Page 152
9.7. Summary......Page 155
9.8. Bibliography......Page 157
PART 4 Applying the Rasch Model......Page 161
Introduction
......Page 162
10.1. Introduction......Page 163
10.2.1. Conditional probabilities......Page 165
10.2.2. Conditional estimates of the instrument parameters......Page 167
10.2.3. An illustrative small example......Page 169
10.3.1. Thresholds reparameterized to two parameters for each instrument......Page 171
10.3.3. A reparameterization with four parameters......Page 175
10.4.1. The conditional test of fit based on cell frequencies......Page 177
10.4.2. The conditional test of fit based on class intervals......Page 178
10.4.2.1. Degrees of freedom for the conditional test of fit based on class intervals......Page 179
10.4.4. Graphical test of fit based on person estimate......Page 180
10.5.2. Equating through person estimates......Page 181
10.6. Example......Page 182
10.6.2. The test of fit between the data and the model......Page 183
10.6.3.4. Graphical test of fit based on conditioning on total scores......Page 186
10.6.3.5. Graphical test of fit based on person estimates......Page 187
10.6.4. Equated scores based on the parameterization with two moments of the thresholds......Page 188
10.6.4.1. Equated scores conditional on the total score......Page 189
10.6.4.2. Equated scores given the person estimate......Page 190
10.7. Discussion......Page 193
10.8. Bibliography......Page 195
11.1. Introduction......Page 197
11.2. The data set......Page 200
11.3.1. Model assumptions......Page 202
11.3.2. Maximum likelihood estimation and model selection......Page 205
11.3.3. Software details......Page 207
11.3.4. Concluding remarks about the model......Page 208
11.4. Correlation between latent traits......Page 209
11.5. Application results......Page 212
11.6. Acknowledgments......Page 215
11.7. Bibliography......Page 216
12.1. Introduction......Page 219
12.2. An IRT model for modeling inter-rater agreement......Page 220
12.3. Umbilical artery Doppler velocimetry and perinatal mortality......Page 221
12.4.1. Fixed-effects approach......Page 222
12.4.2. Random Effects approach and the median odds ratio......Page 225
12.5. Doppler velocimetry and perinatal mortality......Page 227
12.6. Quantifying the rater agreement in the IRT model......Page 229
12.7. Discussion......Page 231
12.8. Bibliography......Page 232
13.1. Introduction......Page 234
13.2. Likelihood......Page 236
13.3. First step: measurement models......Page 237
13.4. Statistical validation of measurement instrument......Page 240
13.5. Construction of scores......Page 244
13.6.1. Health-related quality of life and housing in europe......Page 245
13.6.2. Use of surrogate in an clinical oncology trial......Page 247
13.7. Latent regression to analyze change between groups......Page 249
13.8. Conclusion......Page 252
13.9. Bibliography......Page 253
14.1. Introduction......Page 255
14.2.1. The multilevel form of the conventional Rasch model for binary items......Page 258
14.2.2. Group comparison and repeated measurement......Page 260
14.2.3. Differential item functioning and local dependence......Page 261
14.3. The analysis of an ad hoc scale......Page 262
14.4. Simulation study......Page 266
14.5. Discussion......Page 270
14.6. Bibliography......Page 273
PART 5 Creating, Translating and Improving Rasch Scales......Page 274
Introduction
......Page 275
15.1. Introduction......Page 276
15.1.1. The emergence of the biopsychosocial model of illness......Page 277
15.1.2. Changes in the consultation process in general medicine......Page 278
15.2. The use of patient-reported outcome questionnaires......Page 279
15.2.1.1. Measures of impairment, activity limitations and participation restrictions......Page 280
15.2.1.2. Health status/health-related quality of life......Page 282
15.2.1.3. Generic and specific questionnaires......Page 283
15.2.2.1. Instrument development standards......Page 285
15.2.2.2. Psychometric and scaling standards......Page 286
15.3.2. Questionnaire development......Page 289
15.5. Conclusions......Page 292
15.6. Bibliography......Page 293
16.1.1. Background......Page 298
16.1.2. Aim of the adaptation process......Page 299
16.3.1. Linguistic issues......Page 300
16.4. Translation methodology......Page 301
16.4.1.1. Situation 1: The forward translation is good......Page 302
16.5.1. Bilingual panel......Page 303
16.5.2. Lay panel......Page 304
16.6.1. Cognitive debriefing interviews......Page 305
16.6.1.3. Reporting on the interviews......Page 306
16.6.2. Determining the psychometric properties of the new language version of themeasure......Page 307
16.6.3. Practice guidelines......Page 308
16.7. Bibliography......Page 310
17.1. Introduction......Page 312
17.2. The RM and the graphical log-linear RM......Page 313
17.3. The scale improvement strategy......Page 315
17.3.1. Choice of modification action......Page 317
17.3.2. Result of applying the scale improvement strategy......Page 320
17.4.1. Results of the GLLRM......Page 321
17.4.2. Results of the subject matter analysis......Page 322
17.4.3. Suggestions according to the strategy......Page 323
17.6. Bibliography......Page 326
PART 6 Analyzing and Reporting Rasch Models......Page 329
18.1. Introduction......Page 330
18.2.3. CONQUEST......Page 331
18.3.1. SAS macro for MML estimation......Page 332
18.4.1. Simulation of Rasch dichotomous items......Page 333
18.4.2. MML estimation using PROC NLMIXED......Page 334
18.4.4. JML estimation using PROC LOGISTIC......Page 335
18.4.6. JML estimation using PROC LOGISTIC......Page 336
18.5. Bibliography......Page 337
19.1.1. Objectives......Page 339
19.1.2. Factors impacting a Rasch analysis report......Page 340
19.1.3. The role of the substantive theory of the latent variable......Page 341
19.2. Suggested elements......Page 342
19.2.2. Response format and scoring......Page 343
19.2.3. Sample and sampling design......Page 344
19.2.5. Measurement model and technical aspects......Page 345
19.2.6. Fit analysis......Page 346
19.2.8. Item fit assessment......Page 347
19.2.9. Person fit assessment......Page 348
19.2.11. Validated scale......Page 349
19.2.12. Application and usefulness......Page 350
19.2.13. Further issues......Page 351
19.3. Bibliography......Page 352
List of Authors......Page 354
Index......Page 356