Forms the unit-by-unit variance-covariance matrix for specified variance components in a `REML`

model (R.W. Payne).

### Options

`FIXED` = formula |
Fixed model terms; default `*` |
---|---|

`CONSTANT` = string token |
How to treat the constant term (`estimate` , `omit` ); default `esti` |

`FACTORIAL` = scalar |
Limit on the number of factors or covariates in each fixed term; default 3 |

`SEED` = scalar |
Seed for the random numbers used to generate a dummy y-variate; default 12345 |

### Parameters

`RANDOM` = formula structures |
Random model terms |
---|---|

`COMPONENTS` = variates |
Values for the variance components and residual variance |

`UVCOVARIANCE` = symmetric matrices |
Saves the unit-by-unit variance-covariance matrices |

### Description

Procedure `VBOOTSTRAP`

assesses the significance of for fixed terms in a `REML`

analysis, by using a parametric bootstrap. The bootstrap samples are generated from a multivariate Normal distribution with dimension equal to the number of units in the analysis, and this requires a unit-by-unit variance-covariance matrix.

If you want to take the variance-covariance matrix from a previous analysis, this can be done by using the `UVCOVARIANCE`

option of `VKEEP`

. `VUVCOVARIANCE`

provides a solution for the situation where there is no suitable previous analysis, but you can make reasonable assumptions about the likely sizes of the variance components. Note, however, that it cannot handle covariance models.

The `RANDOM`

parameter specifies a formula structure, defining the random model. This may also contain the residual term, but that is not essential. If it is not present, the residual is added as the final model term. The `COMPONENTS`

parameter specifies the variance components for the random terms, including the residual variance (at the end, if `VUVCOVARIANCE`

needs to add this to the `RANDOM`

formula). The `UVCOVARIANCE`

parameter saves the unit-by-unit variance-covariance matrix.

The `FIXED`

, `CONSTANT`

and `FACTORIAL`

options define the fixed model in the usual way. (See `VCOMPONENTS`

.) The `SEED`

option provides a seed for random numbers (default 12345). These are used to generate a dummy y-variate, that is used in a `REML`

analysis inside the procedure to calculate `UVCOVARIANCE`

.

Options: `FIXED`

, `CONSTANT`

, `FACTORIAL`

, `SEED`

.

Parameters: `RANDOM`

, `COMPONENTS`

, `UVCOVARIANCE`

.

### Method

`UVCOVARIANCE`

obtains the unit-by-unit variance-covariance matrix by using the `COMPONENTS`

as initial values for the random terms in `VCOMPONENTS`

, and performing a `REML`

analysis with the number of iterations set to zero. The y-variate for the analysis contains Normally distributed random numbers, generated with the specified `SEED`

.

### See also

Directive: `REML`

, `VCOMPONENTS`

.

Procedure: `VBOOTSTRAP`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VUVCOVARIANCE example',!t('Split plot design, see the',\ 'Guide to Genstat, Part 2, Section 4.2.1.'); STYLE=meta,plain SPLOAD [PRINT=*] '%gendir%/data/Oats.gsh' " Form unit-by-unit variance-covariance matrix, assuming variance components of 200 for blocks and 100 for whole-plots within blocks, and a residual variance of 150." VUVCOVARIANCE [FIXED=variety*nitrogen] !f(blocks/wplots/subplots);\ COMPONENTS=!(200,100,150); UVCOVARIANCE=uvcov PRINT [RLWIDTH=5] uvcov; FIELD=9