Generates an inverse relationship matrix for use when fitting animal or plant breeding models by `REML`

.

### Options

`SEX` = string token |
Possible sex categories of parents (`fixed` , `either` ); default `fixe` |
---|---|

`UNKNOWN` = scalar |
Value to be treated as unknown |

### Parameters

`INDIVIDUALS` = factors |
Individuals on which data has been measured |
---|---|

`MALEPARENTS` = factors |
Male parents of the progeny |

`FEMALEPARENTS` = factors |
Female parents of the progeny |

`INVERSE` = pointer |
Inverse relationship matrix in sparse matrix form |

`POPULATION` = variates |
Full list of identifiers generated from the individuals and parents |

### Description

`VPEDIGREE`

is used to generate a sparse inverse relationship matrix for use when fitting animal (or plant) breeding models by `REML`

. The algorithm requires three parallel factors as input. The numerical levels of these factors must give identifiers for the individuals from which data are available (`INDIVIDUALS`

) and the identifiers for the male and female parents for each individual (`MALEPARENTS`

and `FEMALEPARENTS`

). Note that an individual may appear as both progeny and a parent (for example, when data has been taken from several generations) and conversely, that if an identifier appears in more than one list then it is assumed to refer to a single individual. Also, the algorithm does not take account of labels, so where textual labels are used the labels vectors of the three factors should be identical in order to generate matching levels vectors and thus avoid errors. A complete list of all individuals in the three factors is compiled and can be saved using the `POPULATION `

option, and on output, the three factors will be redefined with this list as their levels vector.

The inverse relationship matrix that is generated is held in a special sparse matrix form (that is, only non-zero values are stored), using a pointer. This is usable in the `VSTRUCTURE`

directive but not, currently, elsewhere in Genstat. The second element of the pointer is a variate storing the non-zero values of the inverse matrix in lower-triangular order. The first element of the pointer is an integer index vector. This vector is not a standard Genstat data structure, and so cannot be used except by `VSTRUCTURE`

.

By default, it is assumed that an individual can act as either a male or female parent but not both. Option `SEX=either`

can be used to specify that individuals can act as both male and female parents. This may be useful, for example, in plant breeding analyses.

Missing values in any of the factors will be treated as coding for unknown individuals. Option `UNKNOWN`

allows you to specify an additional scalar value used to represent unknown individuals.

Options: `SEX`

, `UNKNOWN`

.

Parameters: `INDIVIDUALS`

, `MALEPARENTS`

, `FEMALEPARENTS`

, `INVERSE`

, `POPULATION`

.

### Action with `RESTRICT`

`VPEDIGREE`

ignores any restrictions on the factors.

### See also

Directives: `REML`

, `VCOMPONENTS`

, `VSTRUCTURE`

, `VRESIDUAL`

, `VSTATUS`

.

Procedure: `VFPEDIGREE`

.

Commands for: REML analysis of linear mixed models.

### Example

" Example REML-6: genetic analysis example (Harvey, W.R. (1977). Users' guide to LSML76)." SPLOAD '%GENDIR%/Examples/harvey.gsh' VPEDIGREE [UNKNOWN=0] INDIVIDUALS=Calf; MALEPARENTS=Sire; FEMALEPARENTS=Dam;\ INVERSE=inv; POPULATION=pop VCOMPONENTS [FIXED=Line] RANDOM=Calf VSTRUCTURE [TERMS=Calf] MODEL=fixed; INVERSE=inv REML [PRINT=model,components,effects,means,vcovariance,Waldtests]\ Y=Y3; SAVE=harvey " Calculate heritability " VKEEP [VESTIMATE=vestim] CALCULATE h2 = vestim$[1]/(1+vestim$[1]) PRINT 22; HEADING='Heritability'