Modelling binary data / David Collett.

Format:

Book

Author/Creator:

Collett, D., 1952-

Series:

Texts in statistical science

Chapman & Hall/CRC texts in statistical science series

Language:

English

Subjects (All):

Analysis of variance.

Distribution (Probability theory).

Linear models (Statistics).

Analysis of Variance.

Linear Models.

Medical Subjects:

Analysis of Variance.

Linear Models.

Physical Description:

387 pages : illustrations ; 24 cm.

Edition:

Second edition.

Place of Publication:

Boca Raton : Chapman & Hall/CRC, [2003]

Contents:

1.1 Some examples 1

1.2 The scope of this book 14

1.3 Use of statistical software 15

2 Statistical inference for binary data 19

2.1 The binomial distribution 19

2.2 Inference about the success probability 23

2.3 Comparison of two proportions 31

2.4 Comparison of two or more proportions 38

3 Models for binary and binomial data 45

3.1 Statistical modelling 45

3.2 Linear models 47

3.3 Methods of estimation 50

3.4 Fitting linear models to binomial data 53

3.5 Models for binomial response data 56

3.6 The linear logistic model 58

3.7 Fitting the linear logistic model to binomial data 59

3.8 Goodness of fit of a linear logistic model 65

3.9 Comparing linear logistic models 71

3.10 Linear trend in proportions 78

3.11 Comparing stimulus-response relationships 81

3.12 Non-convergence and overfitting 85

3.13 Some other goodness of fit statistics 87

3.14 Strategy for model selection 91

3.15 Predicting a binary response probability 98

4 Bioassay and some other applications 103

4.1 The tolerance distribution 103

4.2 Estimating an effective dose 106

4.3 Relative potency 111

4.4 Natural response 114

4.5 Non-linear logistic regression models 118

4.6 Applications of the complementary log-log model 122

5 Model checking 129

5.1 Definition of residuals 130

5.2 Checking the form of the linear predictor 135

5.3 Checking the adequacy of the link function 146

5.4 Identification of outlying observations 150

5.5 Identification of influential observations 154

5.6 Checking the assumption of a binomial distribution 168

5.7 Model checking for binary data 169

6 Overdispersion 195

6.1 Potential causes of overdispersion 195

6.2 Modelling variability in response probabilities 199

6.3 Modelling correlation between binary responses 201

6.4 Modelling overdispersed data 202

6.5 A model with a constant scale parameter 206

6.6 The beta-binomial model 211

7 Modelling data from epidemiological studies 215

7.1 Basic designs for aetiological studies 216

7.2 Measures of association between disease and exposure 219

7.3 Confounding and interaction 223

7.4 The linear logistic model for data from cohort studies 226

7.5 Interpreting the parameters in a linear logistic model 230

7.6 The linear logistic model for data from case-control studies 242

7.7 Matched case-control studies 250

8 Mixed models for binary data 269

8.1 Fixed and random effects 269

8.2 Mixed models for binary data 270

8.3 Multilevel modelling 277

8.4 Mixed models for longitudinal data analysis 284

8.5 Mixed models in meta-analysis 291

8.6 Modelling overdispersion using mixed models 293

9 Exact Methods 303

9.1 Comparison of two proportions using an exact test 303

9.2 Exact logistic regression for a single parameter 307

9.3 Exact hypothesis tests 312

9.4 Exact confidence limits for [beta subscript kappa] 317

9.5 Exact logistic regression for a set of parameters 318

9.6 Some examples 319

10 Some additional topics 325

10.1 Ordered categorical data 325

10.2 Analysis of proportions and percentages 329

10.3 Analysis of rates 330

10.4 Analysis of binary time series 331

10.5 Modelling errors in the measurement of explanatory variables 331

10.6 Multivariate binary data 332

10.7 Analysis of binary data from cross-over trials 333

10.8 Experimental design 333

11 Computer software for modelling binary data 335

11.1 Statistical packages for modelling binary data 335

11.2 Interpretation of computer output 339

11.3 Using packages to perform some non-standard analyses 341

Appendix A Values of logit(p) and probit(p) 351

Appendix B Some derivations 353

B.1 An algorithm for fitting a GLM to binomial data 353

B.2 The likelihood function for a matched case-control study 357

Appendix C Additional data sets 361

C.1 Tonsil size 361

C.2 Toxicity of rotenone 361

C.3 Food poisoning 362

C.4 Analgesic potency of four compounds 362

C.5 Vasoconstriction of the fingers 363

C.6 Treatment of neuralgia 363

C.7 HIV infection 365

C.8 Aplastic anaemia 365

C.9 Cancer of the cervix 367

C.10 Endometrial cancer 367.

Notes:

Includes bibliographical references (pages [369]-378) and indexes.

ISBN:

1584883243

9781584883241

OCLC:

50065016

Publisher Number:

99942974071

Online:

Publisher description