Analyses a series of trials with incomplete-block or row-and-column designs by `REML`

, automatically selecting the best random models (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls what summary output is produced about the models (`deviance` , `aic` , `bic` , `sic` , `dffixed` , `dfrandom` , `change` , `exit` , `best` , `summary` ); default `devi` , `aic` , `sic` , `dfra` , `best` |
---|---|

`PBEST` = string tokens |
Controls the output from the `REML` analysis with the best model (`model` , `components` , `effects` , `means` , `stratumvariances` , `monitoring` , `vcovariance` , `deviance` , `Waldtests` , `missingvalues` , `covariancemodels` , `aic` , `sic` , `bic` ); default `*` i.e. none |

`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 |

`FIXED` = formula |
Fixed model terms; default `*` i.e. none |

`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 |

`EXPERIMENTS` = factor |
Experiment factor |

`REPLICATES` = factor |
Replicate factor, if required |

`BLOCKS` = factor |
Block factor, if required |

`ROWS` = factor |
Row factor, if required |

`COLUMNS` = factor |
Column factor, if required |

`ROWCOORDINATES` = variate or factor |
Row coordinates for fitting trends and spatial models if the design is irregular; if unset, these are defined from the levels of the `ROWS` factor |

`COLCOORDINATES` = variate or factor |
Column coordinates for fitting trends and spatial models if the design is irregular; if unset, these are defined from the levels of the `COLUMNS` factor |

`PLOTFACTOR` = factor |
Factor numbering the plots in the design; if unset, a local factor is defined automatically |

`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` |

`MVINCLUDE` = string tokens |
Whether to include units with missing values in the explanatory factors and variates and/or the y-variates (`explanatory` , `yvariate` ); default `*` i.e. omit units with missing values in either explanatory factors or variates or y-variates |

`VCONSTRAINTS` = string token |
Whether to constrain variance components to be positive (`none` , `positive` ); default `none` |

`RSTRATEGY` = string token |
Strategy for selecting the random model (`all` , `allfeasible` , `fastoptimal` , `optimal` ); default `allf` |

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

`TRYSPATIAL` = string token |
Whether to try spatial models (`always` , `ifregular` ); default `*` i.e. no spatial models |

`TRYTRENDS` = string token |
Whether to see whether row and column trends are needed in the fixed model (`yes` , `no` ); default `no` |

`SPATIALFACTOR` = factor |
Factor to use to define the term for a 2-dimensional power-distance model; if unset, a local factor is defined automatically |

### Parameters

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

`MODELDEFINITIONS` = pointers |
Saves definitions of the best models for use by `VAMETA` |

`EXIT` = variates |
Exit status of the best models (zero if successful) |

`SAVE` = pointers |
`REML` save structures for the best analysis of each experiment |

### Description

`VASERIES`

performs mixed-model analyses of a series of trials with either incomplete-block or row-and-column designs

An *incomplete-block design* is one where the blocks each have too few units to contain one of the treatments. In the context of a `REML`

analysis, the treatment factors are the fixed factors. So this is to say that the blocks are unable each to contain a unit with every combination of levels of the fixed factors.

A *row-and-column design* is a design used for field trials, where the plots are set out in a rectangular grid. Often this is a regular grid, where the rows and columns are equally spaced, and there are no gaps, but irregular arrangements can be handled too.

`VASERIES`

analyses each trial (or experiment), using `REML`

, trying a range of appropriate random models. It then selects the best one according to either their Akaike or Schwarz (Bayesian) information coefficients.

The `EXPERIMENTS`

option specifies a factor to identify the individual trials (or experiments). The block factor is specified by the `BLOCKS`

option, and the row and column factors are specified by the `ROWS`

and `COLUMNS`

options respectively. If all the experiments have incomplete-block designs, the `ROWS`

and `COLUMNS`

options need not be specified, and `BLOCKS`

need not be specified if they are all row-and-column designs. If there is a mixture, the row and column factors should either have only one level or missing values in each of the block designs, and the block factor should have only one level or missing values in each row-and-column design.

You can use the `ROWCOORDINATES`

and `COLCOORDINATES`

options to specify variates or factors giving the actual positions of the plots in a row-and-column design. These are needed if you want to fit row or column trends (i.e. covariates) in the fixed model, or to fit a spatial covariance model when the plots are on an irregular grid. The values of the `ROWS`

and `COLUMNS`

factors are used as defaults, if `ROWCOORDINATES`

and `COLCOORDINATES`

are not set. Their values are also used as defaults if `ROWCOORDINATES`

or `COLCOORDINATES`

are set to variates or factors with no values; the variates or factors are then defined to contain those values.

The `PLOTFACTOR`

option allows you to specify a factor to index the plots, which is needed to specify a power-distance model, or to include a measurement-error term when fitting spatial models to plots on a regular grid. If this is not set, a local factor called `plots`

is set up automatically.

Some designs are *resolvable*. The field can then be divided into sections in which each treatment is replicated once. These replicates can be useful while the experiment is taking place. For example, if several operators are needed to make observations of the plots, it is usual to get each one to observe the plots of a complete replicate. Then any operator differences will be included in the between-replicate variation, and will not add to the variability of the treatment estimates. Of course it can be useful to include a replicate factor even if the “replicates” are not exact, e.g. if some of the treatments do not occur at every level of the replicate factor.

The replicate factor is specified by the `REPLICATES`

option. Note, it is assumed that the blocks, rows and columns are still numbered across the experiment, rather than within replicates.

The `FIXED`

option specifies the fixed terms to be fitted in the analysis. The default fixed model consists of just the constant term, which then becomes the grand mean. The constant term can be omitted by setting option `CONSTANT=omit`

, provided a fixed model has been specified. The `FACTORIAL`

option sets a limit on the number of factors and variates allowed in each fixed term (default 3); any term containing more than that number is deleted from the model. The `RANDOM`

option allows you to specify any extra random terms to include (in addition to replicates and blocks-within-replicates). The `VCONSTRAINTS`

option allows you to constrain the variance components to be positive; by default they are not constrained.

The `TRYSPATIAL`

option indicates whether to try fitting spatial models for row-and-column designs, with settings:

`always` |
always tries to fit them, |
---|---|

`ifregular` |
fit them only if the plots are on a regular grid. |

With the default, `TRYSPATIAL=*`

, no spatial models are fitted. For a regular grid, `VRCBEST`

tries models with order 1 auto-regressive structures on the rows and/or the columns of the design, provided there are more than four rows or columns, respectively. For an irregular grid, if there are more than four rows and more four columns, it tries an anisotropic power-distance model using Euclidean distance. Otherwise, if there is only one dimension with more than four coordinates, it tries an isotropic power-distance model (again using Euclidean distance).

The `SPATIALFACTOR`

option allows you to specify a factor to use to define the term required for a two-dimensional power-distance model. If this is not set, a local factor called `RowColumn2d`

is used.

You can set option `TRYTRENDS=yes`

to see whether row and column trends (i.e. covariates) are needed in the fixed model for a row-and-column design. By default this is not done.

The response variate for the analysis must be specified by the `Y`

parameter. A model-definition structure for the best model can be saved, in a pointer, by the `BESTMODEL`

parameter; the `VMODEL`

procedure can use this to define the model (using the `VCOMPONENTS`

and `VSTRUCTURE`

directives) so that you can reanalyse it yourself using the `REML`

directive. Alternatively, you can save the `REML`

save structure from the analysis with the best model using the `SAVE`

parameter.

The `MVINCLUDE`

option controls whether units with missing values in the explanatory factors and variates and/or the y-variate are included in the analysis, as in the `REML`

directive.

The `RSTRATEGY`

option selects the strategy to use to determine the random model for each trial, with the following settings.

`all` |
fits the full random model. This is appropriate if the random factors played a key role in the design and its randomization. For example, some factors may have been applied to complete rows or complete columns of a row-and-column-design (as in a strip-block design). |
---|---|

`allfeasible` |
tries to fit the full random model. If this is not possible, it tries models removing first one random term, then two and so on, until successful. |

`fastoptimal` |
follows an automatic strategy that aims to find the best random model for a row-and-column design without having to fit all of them. So, for example, it does not try models that include a row main effect as well as a spatial covariance model along rows. This setting is the same as the `optimal` setting for a block design |

`optimal` |
tries all feasible random models. With row-and-column designs this may take a while, and so may be best left for the occasions when you are unsure what to do, or want to check the result from an automatic search. |

`VASERIES`

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 default is `RSTRATEGY=allfeasible`

.

The `METHOD`

option specifies how to assess the random (and spatial) models

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

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

The `PRINT`

option specifies the summary output to be produced about the models. 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 also an extra setting `best`

which prints the description of the best model, and a setting `summary`

which summarizes all the best models at the end of the output. The default is to print the best description, together with the deviance, the Akaike and Schwarz (Bayesian) information coefficients and the number of degrees of all the random models.

The `PBEST`

option specifies the output to be produced from the `REML`

analysis with the best model. Similarly, the `PTRY`

option indicates what output should be produced for each candidate random model when it is tried. Their settings are mainly the same as those of the `PRINT`

option of the `REML`

directive. There are also extra settings `aic`

and `sic`

(with a synonym `bic`

) to print the Akaike and Schwarz (Bayesian) information coefficients, respectively. The default for both these options is to produce no output.

The `PTERMS`

option operates as in `REML`

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

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.

The `Y`

parameter specifies the response variate. The `SAVE`

parameter can save pointer containing a `REML`

save structure from the analysis of the best model for each experiment, so that you can generate further output. The `MODELDEFINITIONS`

parameter can save a pointer to define the models, that can be used by the `VAMETA`

procedure to produce a meta analysis combining information from all the experiments. `MODELDEFINITIONS[0]`

stores the various factors and variates involved in the models, and `MODELDEFINITIONS[i]`

is a model-definition structure for the best model for the *i*th experiment (see the `VFMODEL`

and `VFSTRUCTURE`

procedures for details). The `EXIT`

parameter allows you to save variate containing a code from `REML`

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

You can use procedure `VASDISPLAY`

to display further output from the analyses of any of the experiments, and procedure `VASKEEP`

to save information into Genstat data structures.

Options: `PRINT`

, `PBEST`

, `PTRY`

, `FIXED`

, `RANDOM`

, `CONSTANT`

, `FACTORIAL`

, `EXPERIMENTS`

, `REPLICATES`

, `BLOCKS`

, `ROWS`

, `COLUMNS`

, `ROWCOORDINATES`

, `COLCOORDINATES`

, `PLOTFACTOR`

, `PTERMS`

, `PSE`

, `MVINCLUDE`

, `VCONSTRAINTS`

, `RSTRATEGY`

, `METHOD`

, `TRYSPATIAL`

, `TRYTRENDS`

, `SPATIALFACTOR`

.

Parameters: `Y`

, `MODELDEFINITIONS`

, `EXIT`

, `SAVE`

.

### Method

The `VABLOCKDESIGN`

procedure is used to decide on the best model for experiments with incomplete-block designs, and the `VAROWCOLUMNDESIGN`

procedure is used for those with row-and-column designs.

### See also

Directives: `REML`

, `VCOMPONENTS`

, `VSTRUCTURE`

.

Procedures: `VABLOCKDESIGN`

, `VAMETA`

, `VAOPTIONS`

, `VAROWCOLUMNDESIGN`

, `VASDISPLAY`

, `VASKEEP`

, `VASMEANS`

, `VMODEL`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VASERIES example'; STYLE=meta SPLOAD '%gendir%/examples/Vaseries.gsh' VASERIES [PRINT=best,deviance,aic,bic,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 PRINT modeldefs[1...3]['description']