### Table of Contents

# Specialized analyses with WOMBAT

This page provides some hints for non-standard analyses.

### Fitting a factor-analytic model

WOMBAT can accommodate a factor-analytic model for the structure of covariance matrices of random effects. While there is no explicit option for this structure, it is easily fitted indirectly.
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### Dealing with `clones'

In some instances we have clones, i.e. subjects which are genetically identical.
For instance, monozygotic twins are naturally occuring clones. If these individuals have different identity codes and the same parents, WOMBAT will simply treat them as ordinary full-sibs. Alternatively, if all members of the clone are given the same identity, records on all members of the clone are treated as if they were repeated observations for the same individual. That is not correct either - hence special action needs to be taken.
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### Fitting X-linked genetic effects

WOMBAT has an in-built facility to allow for X-linked genetic effects. In brief,
this is fitted as an additional random effect and WOMBAT can calculate the appropriate inbreeding coefficients and set up
the inverse of the corresponding relationship matrix directly from the list of pedigree information
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### Fitting imprinting effects

WOMBAT readily allows for models fitting imprinting effects. These are best fitted as gametic effects, setting up the inverse of the gametic relationship matrix externally and supplying it to the analysis as `.gin`

file.
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### GWAS analyses

WOMBAT allows for efficient GWAS type analyses for a mixed model fitting SNP effects as linear covariables. This exploits that, for complete (or imputed) genotype information only the part of mixed model equations due to the SNP effects changes as different SNPs are considered. ** --- MORE ---**

### "Single step" genomic BLUP

WOMBAT offers special options to solve sets of mixed model equations for so-called single step anlyses, combining information on genotyped and non-genotyped individuals.

Currently, there are three different implementations, with varying degree of optimisation and testing

- The first is simply an analysis in which the inverse of the combined relationship matrix, ${\bf H}^{-1} $, is suplied in a
`*.gin`

file. It is invoked with the run option`—-s1step`

.

- As for run option
`– –solvit`

, the mixed model equations are set up once and stored in core. - A special feature for the single step analysis is that the part of the coefficient matrix in the mixed model equations pertaining to genotyped animals is stored as a dense submatrix. This implies substantial RAM requirements for large analyses, but allows efficient, multi-threaded library routine for dense matrix manipulations to be exploited.
- Iterative solutions are obtained using a pre-conditioned conjugate gradient algorithm with a choice of diagonal, block-diagonal of SSOR (default) preconditioning scheme.

- A low RAM alternative is invoked via run option
`—-s2step`

: This employs a PCG algorithm with diagonal preconditioner, using 'iteration on data' instead of in-core storage of the mixed model equations.

It requires pedigree information (to set up the inverse of the numerator relationship matrix) and the 'add-on' part in the combined relationship matrix, $ {\bf G}^{-1} - {\bf A}_{22}^{-1}$ as a`*.gin`

file. - Work in progress: An implementation of the `super hybrid model'

### Genomic relationship matrices

WOMBAT provides a (new) module to carry out calculations required to form and invert the genomic relationship matrix or the joint matrix of relationships between non-genotyped and genotyped individuals required for single-step analyses.
This is invoked via run option `—-hinv`

. Documentation on the numerous options available can be found as part of
Example20.

### Semiparametric regression

- bib
@BOOK{rupp03, author = {Ruppert, D. and Wand, M. P. and Carroll, R. J.}, title = {Semiparametric Regression}, year = {2003}, publisher = {Cambridge University Press}, address = {New York} } @ARTICLE{Cante05, author = {Cantet, R. J. C. and Birchmeier, A. N. and Cayo, A. W. Canaza and Fioretti, C.}, pages = {2482--2494}, title = {Semiparametric animal models via penalized splines as alternatives to models with contemporary groups}, journal = {J. Anim. Sci.}, volume = {83}, number = {11}, year = {2005} }