Performs a `REML`

meta analysis of a series of trials, previously analysed by `VASERIES`

(R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`model` , `components` , `effects` , `means` , `stratumvariances` , `monitoring` , `vcovariance` , `deviance` , `Waldtests` , `missingvalues` , `covariancemodels` , `aic` , `sic` , `bic` ); default `mode` , `comp` , `Wald` |
---|---|

`PTRY` = string tokens |
Controls the output to present to present from the `REML` analysis used to try each model (`model` , `components` , `effects` , `means` , `stratumvariances` , `monitoring` , `vcovariance` , `deviance` , `Waldtests` , `missingvalues` , `covariancemodels` , `aic` , `sic` , `bic` ); default `*` i.e. none |

`PRECOVERY` = string tokens |
Controls what summary output is produced about the models that are tried during recovery (`deviance` , `aic` , `bic` , `sic` , `dffixed` , `dfrandom` , `change` , `exit` , `best` ); default `devi` , `aic` , `sic` , `dfra` , `best` |

`FIXED` = formula |
Fixed model terms; if unset, these are taken from the `MODELSTRUCTURES` |

`RANDOM` = formula |
Additional random model terms; default `*` i.e. none |

`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 |

`PTERMS` = formula |
Terms (fixed or random) for which effects or means are to be printed; default `*` implies all the fixed terms |

`PSE` = string token |
Standard errors to be printed with tables of effects and means (`differences` , `estimates` , `alldifferences` , `allestimates` , `none` ); default `diff` |

`RECOVER` = string token |
Whether to try to recover with a simpler random model if `REML` cannot fit the model (`yes` , `no` ); default `no` |

`METHOD` = string token |
How to choose the best model during recovery (`aic` , `sic` , `bic` ); default `sic` |

### Parameters

`Y` = variates |
Response variates |
---|---|

`MODELDEFINITIONS` = pointers |
Descriptions of the models for each y-variate, saved from `VASERIES` |

`EXIT` = scalars |
Exit status for the fit (zero if successful) |

`SAVE` = vsaves |
`REML` save structure from the analysis of each y-variate |

### Description

`VAMETA`

can perform a `REML`

meta analysis of a series of trials with either incomplete-block or row-and-column designs. The trials must previously have been analysed by the `VASERIES`

procedure, to determine the best random model to use with each trial. Details of the models must be saved using the `MODELDEFINITIONS`

parameter of `VASERIES`

, and then supplied to `VAMETA`

using its own `MODELDEFINITIONS`

parameter. However, you can redefine the fixed model to fit in the meta analysis, and the action to take with the constant term (estimate or omit), by setting the `FIXED`

and `CONSTANT`

options, respectively. The `FACTORIAL`

option sets a limit on the number of factors and variates allowed in each term defined by `FIXED`

(default 3). You can also use the `RANDOM`

option to specify some additional random terms to include in the analysis. Note: these terms are removed, if necessary, from the random terms selected by `VASERIES`

to be fitted independently for any trial.

The `PRINT`

option specifies the output to be produced from the analysis. The settings are mainly the same as those of the `PRINT`

option of the `REML`

directive but with extra settings `aic`

and `sic`

(with a synonym `bic`

) to print the Akaike and Schwarz (Bayesian) information coefficients, respectively. The default is to print model descriptions, estimated variance components and Wald or F tests for fixed effects.

The `Y`

parameter specifies the response variate. The `SAVE`

parameter can save pointer containing a `REML`

save structure from the analysis that can be used e.g. to display further output using the `VDISPLAY`

directive. The `EXIT`

parameter allows you to save a code from `REML`

, giving the “exit status” of the fit (zero if successful).

The random models in meta analysis can become complicated, and `REML`

may be unable to achieve a successful fit if there are more random terms than are actually needed to explain the random variation.(The `REML`

likelihood may be too flat for any clear optimum to be found.) You can guard against this situation by setting option `RECOVER=yes`

. `VAMETA`

then tries models removing first one random term (and any associated spatial model), then two and so on, until successful. Note: it regards a model as successful, if the `REML`

directive returns an exit status of zero (i.e. successful fitting) and there are no bound or aliased variance parameters.

The `METHOD`

option specifies how to choose the random (and spatial) model if there is more than one possible model with the same number of random terms removed:

`aic` |
uses their Akaike information coefficients, |
---|---|

`sic` or `bic` |
uses their Schwarz (Bayesian) information coefficients (default). |

The `PRECOVERY`

option specifies the summary output to be produced about the models that are fitted during recovery. The settings are mainly the same as those of the `VRACCUMULATE`

procedure (which is used to store and then print details of the analyses). There is an extra setting, `best`

, to print the description of the best model. The default is to print the best description, together with the deviance, the Akaike and Schwarz (Bayesian) information coefficients and the number of degrees, for all the models. The `PRTRY`

option, with the same settings as `PRINT`

, controls output from each individual analysis.

The `PTERMS`

option operates as in `REML`

, to specify the terms whose means and effects are printed by `PRINT`

and `PTRY`

; the default is all the fixed terms. Likewise, the `PSE`

option controls the type of standard error that is displayed with the means and effects; the default is to give a summary of the standard errors of differences.

Options: `PRINT`

, `PTRY`

, `PRECOVERY`

, `FIXED`

, `RANDOM`

, `CONSTANT`

, `FACTORIAL`

, `PTERMS`

, `PSE`

, `RECOVER`

, `METHOD`

.

Parameters: `Y`

, `MODELDEFINITIONS`

, `EXIT`

, `SAVE`

.

### Method

The `VRMETAMODEL`

procedure is used to define the random model for the meta analysis, if there are random terms that need to be fitted for only some of the trials. The `VRESIDUAL`

directive is used to define spatial covariance models if required in any of the trials.

### See also

Directives: `REML`

, `VDISPLAY`

, `VKEEP`

, `VRESIDUAL`

.

Procedures: `VASERIES`

, `VMETA`

, `VRMETAMODEL`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VAMETA example'; STYLE=meta SPLOAD '%gendir%/examples/Vaseries.gsh' " find best random model for each trial " VASERIES [PRINT=best,devi,aic,sic,dfrandom,summary;\ PBEST=model,components,wald; FIXED=entry;\ EXPERIMENTS=site; ROWS=row; COLUMNS=column; BLOCKS=block;\ MVINCLUDE=yvariate; TRYSPATIAL=ifregular; TRYTRENDS=yes;\ RSTRATEGY=fastoptimal; VCONSTRAINTS=positive]\ yield; MODELDEFINITIONS=modeldefs; SAVE=save " meta analysis with these models " VAMETA [PRINT=model,components,wald] Y=yield; MODELDEFINITIONS=modeldefs;\ SAVE=savemeta