WOMBAT Example 15: Pooling results from analyses by parts

This example illustrates how to pool estimates of covariance
components by (penalized) maximum likelihood using WOMBAT.

The example is comprised of 14 traits, with 6 traits measured on few
animals and the remaining records representing 4 traits with measures
on males and females treated as different traits (Results from Meyer
2007; J. Anim. Breed. Genet, 124:50-64). There are results from 76
bivariate and one six-variate analysis to be combined. Due to traits
measured on different subsets of animals (sexes) there are a number of
residual covariances which are to be fixed at zero.

Parts: Results from all 77 part analyses, as written out by WOMBAT and
   joint file of all results.

A: Using results written out by WOMBAT & a `full' parameter file: 
   Unpenalized analysis

A1: as A, but results from part analyses are summarized in a single 
   file and a `minimum' parameter file is used.

A2: as A1, but specifying the pseduo pedigree structure explicitly
   (NB: different value for likelihood compared to A and A1 but
    comparable results; due to somewhat different calculations).

B: as A, but carrying out two penalised analyses in addition.

C: as A, but carrying out a penalised analysis with 'beta' penalty on
    canonical eigenvalues in addition.

D: as A, but pooling (no penalty) results for *one* covariance matrix 
   at a time using run option --itsum to invoke Mantysaari (1999)'s 
   method of iterative summation of expanded part matrices.
   Need to copy output file PDBestPoint to BestPoint and run with option
   --best to generate report on genetic parameter estimates.

E: as A, but pooling only residual covariances by converting part estimates
   to pseudo observations, as suggested by Thompson et al 2005, and using
   these in a standard REML run

RNote_WOMBATPool.pdf: Notes attempting a brief tutorial on pooling and how
   to do this in WOMBAT. This includes an illustration for 4 traits, as
   given in Example4/E (download separately).



