Defines the residual term for a `REML`

analysis, or the residual term for an experiment within a meta-analysis (combined analysis of several experiments).

### Options

`EXPERIMENT` = scalar |
Level of the `EXPERIMENTS` factor for which the residual is being defined |
---|---|

`TERM` = formula |
Model term to be used as the residual |

`FORMATION` = string token |
Whether the structure is formed by direct product construction or by definition of the whole matrix (`direct` , `whole` ); default `dire` |

`VARIANCE` = scalar |
Allows an initial estimate to be provided for the residual variance of the experiment |

`CONSTRAINT` = string token |
Allows the residual variance to be fixed at its initial value (`fix` , `positive` ) default `posi` |

`COORDINATES` = matrix or variates |
Coordinates of the data points to be used in calculating distance-based models |

### Parameters

`MODELTYPE` = string tokens |
Type of covariance model associated with the term(s), or with individual factors in the term(s) if `FORMATION=direct` (`identity` , `fixed` , `AR` , `MA` , `ARMA` , `power` , `boundedlinear` , `circular` , `spherical` , `linearvariance` , `banded` , `correlation` , `antedependence` , `unstructured` , `diagonal` , `uniform` , `FA` , `FAequal` ) default `iden` |
---|---|

`ORDER` = scalar |
Order of model |

`HETEROGENEITY` = string token |
Heterogeneity for correlation matrices (`none` , `outside` ); default `none` |

`METRIC` = string token |
How to calculate distances when `MODEL=power` (`cityblock` , `squared` , `euclidean` ); default `city` |

`FACTOR` = factors |
Factors over which to form direct products |

`MATRIX` = identifiers |
To define matrix values for the term or the factors when `MODEL=fixed` |

`INVERSE` = identifiers |
To define values for matrix inverses (instead of the fixed matrices themselves) when `MODEL=fixed` |

`INITIAL` = identifiers |
Initial parameter values for each correlation matrix |

`CONSTRAINTS` = texts |
Texts containing strings `none` , `fix` or `positive` to define constraints for the parameters in each model |

`EQUALITYCONSTRAINTS` = variates |
Non-zero values in the variate indicate groups of parameters whose values are to be constrained to be equal |

### Description

`VRESIDUAL`

is used to define the residual term for a `REML`

analysis or to define separate residual terms for different experiments within a multi-experiment (or meta-) analysis. The `TERM`

option is used to specify the formula for the residual term. This term need not have been specified previously by the `VCOMPONENTS`

statement.

For a single experiment, `VRESIDUAL`

can be used to impose a covariance structure on the residual term. This could also be done by specifying the covariance structure using `VSTRUCTURE`

, but `VRESIDUAL`

has the advantage that the algorithm then checks that the correct residual term is used.

In a multi-site experiment, `VRESIDUAL`

can be used to specify a different residual model for each separate experiment. The `EXPERIMENT`

option is used to define the experiment(s) for which the model is to be used.

The `VARIANCE`

option is used to give an initial value for the residual variance in the current experiment(s). You can set option `CONSTRAINT=fix`

to fix the residual variance at the initial value rather than estimating it (as a positive value).

The definition of the residual terms then follows mainly as for the definition of correlated error terms through `VSTRUCTURE`

The exception is that power models can be defined only in terms of the coordinates of the data points, not by specifying coordinates for the factor levels. (So the `DISTANCES`

and `COORDINATES`

parameters of `VSTRUCTURE`

are not present in `VRESIDUAL`

.)

For a multi-experiment analysis, the factors and variates for the separate experiments should be concatenated into structures which run over all the experiments. For example, consider an experiment set up at two sites to compare a set of 24 varieties in four replicates. In one site the experiment was laid out as a grid of eight rows by 12 columns, in the other a grid of 16 rows by six columns was used. In these circumstances, a single set of factors (of length 192) can be used to specify the design, using factors to describe variety, rows and columns, plus a factor `expt`

defining the allocation of units to experiments.

`VCOMPONENTS [FIXED=Variety; EXPERIMENTS=Expt] `

`VRESIDUAL [EXPERIMENT=1; TERM=Row.Col] MODEL=AR,AR;\`

` ORDER=1,1; FACTOR=Row,Col`

`VRESIDUAL [EXPERIMENT=2; TERM=Row.Col] MODEL=AR,AR;\`

` ORDER=1,1; FACTOR=Row,Col`

Where some factors differ between experiments, these should be defined on the units relevant to the appropriate experiment(s) and missing elsewhere. When an `EXPERIMENTS`

factor has been defined, the default action of the `MVINCLUDE`

option of `REML`

is changed to include units with missing y-values and missing factor levels.

Options: `EXPERIMENT`

, `TERM`

, `FORMATION`

, `VARIANCE`

, `CONSTRAINT`

, `COORDINATES`

Parameters: `MODEL`

, `ORDER`

, `HETEROGENEITY`

, `METRIC`

, `FACTOR`

, `MATRIX`

, `INVERSE`

, `INITIAL`

, `CONSTRAINTS`

, `EQUALITYCONSTRAINTS`

.

### See also

Directives: `REML`

, `VCOMPONENTS`

, `VSTRUCTURE`

, `VPEDIGREE`

, `VSTATUS`

.

Procedures: `VAMETA`

, `VRMETAMODEL`

.

Commands for: REML analysis of linear mixed models.