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Statistical Models for the Precision of Categorical Measurement
van Wieringen, W.N.
Publication date
2003
Link to publication
Citation for published version (APA):
van Wieringen, W. N. (2003). Statistical Models for the Precision of Categorical
Measurement.
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Contents s
11 Levels and quality of measurement 1
1.11 Definition of measurement 1 1.22 Levels of measurement 2 1.33 Quality of measurement 4 1.44 Objective and motivation of the thesis 6
1.55 Outline of the thesis 6 1.66 An introductory example 6
1.6.11 Mathematical model 7 1.6.22 Statistical analysis 10 1.6.33 Criteria for measurement error 11
22 The assessment of precision of binary measurement systems 13
2.11 Latent class model 13 2.1.11 Latent class method 15
2.22 Alternative methods 16 2.2.11 Measure of agreement based on kappa 16
2.2.22 Kappa for multiple raters 17 2.2.33 Kappa statistic from the perspective of the latent class model 18
2.2.44 Intraclass correlation coefficient 19 2.2.55 The intraclass correlation coefficient from the perspective of the latent
classs model 20 2.2.66 Log-linear model 21
2.2.77 The log-linear model from the perspective of the latent class model 22
2.33 Example 23 2.44 Conclusion 25
33 On the latent class model 27
3.11 The latent class model 27
3.22 Identifiability 28 3.2.11 Main result 29 3.2.22 Mixed factorial moments 30
3.2.33 Proof of theorem 2 31 3.33 Estimation of the model parameters 35
3.3.11 Method of moments 35 3.3.22 Method of maximum likelihood 39
3.44 Confidence intervals 45 3.55 Goodness-of-fit 47
Appendixx A 49 Appendixx B 52 Appendixx C 58
44 The assessment of precision of ordinal measurement systems 61
4.11 Introduction 61 4.22 Inventory of current methods 62
4.2.11 Intraclass Correlation Coefficient 62
4.2.22 Gauge R&R 63 4.2.33 Kappa 63 4.2.44 Nonparametric methods 64
4.2.55 Other alternatives 65 4.33 MSA for bounded ordinal data 65
4.3.11 Modification of the ICC method 65 4.3.22 Modification of the Kappa method 69 4.3.33 Modification of nonparametric methods 69
4.44 Examples 70 4.4.11 Artificial data set 70
4.4.22 Printer assembly data 71 4.55 Discussion and conclusion 72
4.5.11 Discussion 72 4.5.22 Conclusion 74
Appendixx 75
55 The evaluation of categorical measurement systems in practice 77
5.11 Outline of the investigation 77
5.22 An example 86
Referencess 91 Woordenn van samenvattende aard 95
Woordenn van dank 97 Woordenn aangaande mijn leven 98 8
