Page 9 - Linear Models for the Prediction of Animal Breeding Values

13. Analysis of Ordered Categorical Traits 219
13.1. Introduction 219
13.2. The Threshold Model 220
13.2.1. Defining some functions of the normal distribution 220
13.2.2. Data organization and the threshold model 221
13.2.3. Numerical example 223
13.3. Joint Analysis of Quantitative and Binary Traits 230
13.3.1. Data and model definition 230
13.3.2. Numerical application 234

14. Survival Analysis 240
14.1. Introduction 240
14.2. Functional Survival 240
14.3. Censoring 240
14.4. Models for Analysis of Survival 241
14.4.1. Linear models 241
14.4.2. Random regression models for survival 241
14.4.3. Proportional hazard models 243
14.4.4. Non-parametric estimation of the survival function 245
14.4.5. Regression survival models 246
14.4.6. Mixed survival models 247
14.4.7. Group data survival model 250

15. Estimation of Genetic Parameters 251
Robin Thompson
15.1. Introduction 251
15.2. Univariate Sire Model 251
15.3. Numerical Example of Sire Model 252
15.4. Extended Model 253
15.5. Numerical Example 254
15.6. Animal Model 255
15.7. Numerical Example 257

16. Use of Gibbs Sampling in Variance Component
Estimation and Breeding Value Prediction 260
16.1. Introduction 260
16.2. Univariate Animal Model 261
16.2.1. Prior distributions 261
16.2.2. Joint and full conditional distributions 262
16.2.3. Inferences from the Gibbs sampling output 264
16.2.4. Numerical application 265
16.3. Multivariate Animal Model 266
16.3.1. Prior distributions 267
16.3.2. Conditional probabilities 267
16.3.3. Numerical illustration 269

17. Solving Linear Equations 271
17.1. Introduction 271
17.2. Direct Inversion 271

Contents ix