Forms the random model for a `REML`

meta analysis (R.W. Payne).

**Options **

`RANDOM` = formula structure |
Saves the random model |

`EXPERIMENTSFACTOR` = factor |
Factor defining which units are in each experiment |

`TERMS` = formula |
Specifies terms, if any, to be fitted over the whole data set; default * i.e. none |

### Parameters

`EXPERIMENT` = scalars, variates or texts |
Experiments on which additional random terms are to be fitted |

`LOCALTERMS` = formula structures |
Random terms that are to be fitted only on the corresponding experiment |

`SAVEVECTORS` = pointers |
Saves the factors (and/or any variates) defined to represent the local terms on each experiment |

### Description

In `REML`

meta analyses the designs used in the various experiments need not be identical and, even if they are all the same, the same random model may not be appropriate for every one. `REML`

does allow you to fit different random terms in the different experiments, but their definition can be tedious. For example, if you wanted to include the term `Blocks`

only in experiments 1 and 2 (and with a different variance component in each case), you would need to take two copies of the factor, giving them names (e.g. `Blocks1`

and `Blocks2`

) that will be recognisable in the output. Then, set `Blocks1`

to missing except within experiment 1, and `Blocks2`

to missing except in experiment 2. If you now add `Blocks1 + Blocks2`

to the overall random model, and set option `MVINCLUDE=explanatory`

in the `REML`

statement, the terms `Blocks1`

and `Blocks2`

will each be fitted only in the desired experiment (1 or 2, respectively), and ignored elsewhere. An example is shown in Chapter 2 of the *Guide to REML*.

The process of forming the modified copies of the factors and devising names to label them clearly on the output can be inconvenient. So procedure `VRMETAMODEL`

has been provided to make this clearer and more straightforward. In the output a term like `Reps.Blocks`

, that is to be fitted only e.g. at Rothamsted, will be labelled

`Reps@Rothamsted.Blocks@Rothamsted`

The random model is formed automatically, and can be saved in a formula structure by the `RANDOM`

option. The `EXPERIMENTSFACTOR`

option must specify a factor to indicate which units of the data set belong to each experiment, and the `TERMS`

option can specify random terms that are to be fitted over the whole data set.

The `EXPERIMENT`

parameter lists the experiments where additional random terms are to be fitted, using either the levels or the labels of `EXPERIMENTSFACTOR`

. You can specify a variate or a text with several values, if the terms are to be fitted with the same variance components in more than one experiment.

The LOCALTERMS parameter specifies a formula structure for each experiment to define its additional terms. The factors (and any variates) in the additional terms for each experiment are copied, the required missing values are inserted, and the terms are added to the random model.

By default, the modified copies of the factors and variates that are formed to represent the additional random terms will be unnamed, and exist only as part of the `RANDOM`

model. (The labels that appear in the output are attached to the factors by setting the EXTRA parameter in the `FACTOR`

statement or `VARIATE`

statement that defined them inside `VRMETAMODEL`

.) The `SAVEVECTORS`

parameter allows you to supply a pointer for each experiment, to save its factors (and any variates), so that you use them to refer to the additional random terms e.g. in the `VKEEP`

directive. The elements of each pointer are labelled by the identifiers of the factors or variates in the corresponding local term to simplify their subsequent use.

Options: `RANDOM`

, `EXPERIMENTSFACTOR`

, `TERMS`

.

Parameters: `EXPERIMENT`

, `LOCALTERMS`

, `SAVEVECTORS`

.

### See also

Directive: `REML`

, `VCOMPONENTS`

, `VRESIDUAL`

.

Procedure: `META`

, `VAMETA`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VRMETAMODEL example',\ 'Example from Chapter 2 of Guide to REML.'; STYLE=meta,plain SPLOAD [PRINT=*] '%gendir%/data/MetaFungicide.gsh' " Define additional random terms: block in 1997, block in 1998, and block.wholeplot in 1999." VRMETA [TERMS=year*fungicide*cultivar;\ EXPERIMENTSFACTOR=year; RANDOM=random] 1997,1998,1999;\ LOCALTERMS=!f(block),!f(block),!f(block.wholeplot);\ SAVEVECTORS=svec[1997...1999] VCOMPONENTS [FIXED=fungicide*cultivar; EXPERIMENTS=year] #random REML [MVINCLUDE=explanatory] yield " Save variance components for block in 1998, and block.wholeplot in 1999." VKEEP svec[1998]['block']+svec[1999]['block'].svec[1999]['wholeplot'];\ COMPONENT=vcb1998,vcbw1999 PRINT vcb1998,vcbw1999