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 3.1.1. This generates the
directory WOMBAT/Examples with subdirectories Example
(
).
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
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