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Chapter 9
Worked examples

A number of worked examples are provided to illustrate the use of WOMBAT and, in particular, show how to set up the parameter files.

Installation for the suite of examples is described in section 3.1.4. This generates the directory WOMBAT/Examples with subdirectories Examplen (n = 1,...,9 ).

Each subdirectory contains the data and pedigree files for a particular example, a file WhatIsIt with a brief description of the example, and one or subdirectories for individual runs, A, B, C, ... .

Each ‘run’ directory (A, B, ... ) contains :

(a)
A parameter file (.par)
(b)
The file typescript (generated using the script command) which contains the screen output for the run.
Run time options used can be found at the top of this file.
(c)
The numerous output files generated by WOMBAT.

N.B.: The example data sets have been selected for ease of demonstration, and to allow fairly rapid replication of the example runs. Clearly, most of the data sets used are too small to support estimation of all the parameters fitted, in particular for the higher dimensional analyses shown !

N.B.: Examples runs have been carried out on a 64-bit machine; numbers obtained on 32-bit machine may vary slightly.

Note further that all the example files are LINUX files - you may need to ’translate’ them to DOS format if you plan to run the examples under Windows.

  Example 1
  Example 2
  Example 3
  Example 4
  Example 5
  Example 6
  Example 7
  Example 8
  Example 9

Example 1

This shows a univariate analysis for a simple animal model, fitting a single fixed effect only.

Source: Simulated data; Example 1 from DFREML

Example 2

This shows a bivariate analysis for the case where the same model is fitted for both traits and all traits are recorded for all animals. The model of analysis is an animal model with an additional random effect, and included 3 cross-classified fixed effects.

Source: Data from Edinburgh mouse lines; Example 2 from DFREML

Example 3

This example involves up to six repeated records for a single trait, recorded at different ages. The model of analysis is an animal model with a single fixed effect. Data are analysed :

A
Fitting a univariate ‘repeatability’ model, with age as a covariable
B
Fitting a multivariate analysis with 6 traits
C
Fitting a univariate random regression model

Source: Wokalup selection experiment; Example 3 from DFREML

Example 4

This example shows a four-variate analysis for a simple animal model. Runs show:

A
A ‘standard’ full rank analysis
B
A reduced rank analysis, fitting the first two principal components only
C
A reduced rank analysis using the EM algorithm

Source: Australian beef cattle field data

Example 5

Similar to example 4, but involving 6 traits.

A
A ‘standard’ full rank analysis
B
A reduced rank analysis, fitting the first four principal components

Source: Australian beef cattle data

Example 6

This example involves 4 measurements, with records on different sexes treated as different traits. This gives an eight-variate analysis, with 16 residual covariances equal to zero. The model of analysis is a simple animal model.

A
A full rank analysis with ‘good’ starting values
B
A full rank analysis with ‘bad’ starting values

Source: Australian beef cattle field data

Example 7

This example illustrates the analysis of 4 traits, subject to genetic and permanent environmental effects. The model of analysis involves several crossclassified fixed effects, nested covariables and different effects for different traits.

A
Univariate analysis for trait 1
B
Univariate analysis for trait 2
C
Univariate analysis for trait 2, allowing for a non-zero direct-maternal genetic covariance
D
Bivariate analysis for traits 1 and 2
E
Bivariate analysis for traits 1 and 2, allowing for a non-zero direct-maternal genetic covariance
F
Trivariate analysis for traits 1, 2 and 3
G
Fourvariate analysis of all traits
H
Fourvariate analysis of all traits, not fitting maternal effects for trait 4
I
Reduced rank, fourvariate analysis of all traits, not fitting maternal effects for trait 4

Source: Wokalup selection experiment

Example 8

This is an example of a model where different random effects are fitted for different traits. It is a bivariate analysis of mature cow weights together with gestation length. Mature cow weight involves repeated records per animal, and a permanent environmental effect of the animal is thus fitted for this trait. Gestation length is treated as trait of the calf and assumed to be affected by both genetic and permanent environmental effects.

A
Standard model
B
Equivalent model, using the PEQ option for permanent environmental effects of the animal.

Source: Australian beef cattle field data

Example 9

This example illustrates random regression analyses fitting an additional random effect, using B-splines as basis functions and imposing rank restrictions on estimated covariance functions. Data are monthly records for weights of calves from birth to weaning.

A
Full rank analysis
B
Reduced rank analysis
C
Reduced rank analysis with different ranks

Source: Wokalup selection experiment

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