Page 7 - Linear Models for the Prediction of Animal Breeding Values

6.3. Cholesky Transformation 98
6.3.1. Calculating the transformation matrix and defining the model 98
6.3.2. An illustration 99
6.4. Factor and Principal Component Analysis 101
6.4.1. Factor analysis 102
6.4.2. Principal component analysis 105
6.4.3. Analysis with reduced rank PC model 106

7. Maternal Trait Models: Animal and Reduced Animal Models 109
7.1. Introduction 109
7.2. Animal Model for a Maternal Trait 110
7.2.1. An illustration 110
7.3. Reduced Animal Model with Maternal Effects 115
7.3.1. An illustration 116
7.4. Sire and Maternal Grandsire Model 119

8. Social Interaction Models 121
8.1. Introduction 121
8.2. Animal Model with Social Interaction Effects 123
8.2.1. Illustration of a model with social interaction 125
8.3. Partitioning Evaluations from Associative Models 127
8.4. Analysis Using Correlated Error Structure 128

9. Analysis of Longitudinal Data 130
9.1. Introduction 130
9.2. Fixed Regression Model 131
9.2.1. An illustration 132
9.3. Random Regression Model 136
9.3.1. Numerical application 138
9.3.2. Partitioning animal solutions from random regression model 142
9.3.3. Calculating daughter yield deviations 145
9.3.4. Reliability of breeding values 146
9.3.5. Random regression models with spline function 147
9.3.6. Random regression model for maternal traits 148
9.4. Covariance Functions 149
9.4.1. Fitting a reduced order covariance function 151
9.5. Equivalence of the Random Regression Model
to the Covariance Function 155

10. Use of Genetic Markers in Breeding Value Prediction 156
10.1. Introduction 156
10.2. Defining a Model with Marker Information 156
10.3. Calculating the Covariance Matrix (G ) for MQTL Effects 157
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10.3.1. Numerical application 158
10.4. An Alternative Approach for Calculating G 160
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10.5. Calculating the Inverse of G 161
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10.6. Prediction of Breeding Values with Marker Information 165
10.6.1. An illustration 165

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