The REML algorithm allows you to analyse linear mixed models i.e. linear models that can contain both fixed and random effects. In some applications these are known as “multi-level” models. It can thus be used to analyse unbalanced designs with several error terms (which cannot be analysed by `ANOVA`

). It can also fit random correlation models to describe the covariances between random effects as can arise, for example, in the analysis of repeated measurements or spatial data.

`REML` |
fits a variance-component model by residual (or restricted) maximum likelihood |
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`VCOMPONENTS` |
defines the model for `REML` |

`VCYCLE` |
controls advanced aspects of the `REML` algorithm |

`VDISPLAY` |
displays further output from a `REML` analysis |

`VKEEP` |
copies information from a `REML` analysis into Genstat data structures |

`VSTRUCTURE` |
defines a variance structure for random effects in a `REML` model |

`VPEDIGREE` |
generates an inverse relationship matrix for use when fitting animal or plant breeding models by `REML` |

`VPREDICT` |
forms predictions from a `REML` model |

`VRESIDUAL` |
defines the residual term for a `REML` model |

`VSTATUS` |
prints the current model settings for `REML` |

There are several procedures that may be useful, for example, to define the model, to produce additional output or for other REML-based analyses.

`FCONTRASTS` |
modifies a model formula to contain contrasts of factors |
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`FDIALLEL` |
forms the components of a diallel model for REML or regression |

`F2DRESIDUALVARIOGRAM` |
calculates and plots a 2-dimensional variogram from a 2-dimensional array of residuals |

`TOBIT` |
linear mixed model analysis of data with fixed-threshold censoring |

`VAIC` |
calculates the Akaike and Schwarz (Bayesian) information coefficients for REML |

`VALLSUBSETS` |
fits all subsets of the fixed terms in a REML analysis |

`VAYPARALLEL` |
does the same `REML` analysis for several y-variates, and collates the output |

`VBOOTSTRAP` |
performs a parametric bootstrap of the fixed effects in a `REML` analysis |

`VCRITICAL` |
uses a parametric bootstrap to estimate critical values for a fixed term in a `REML` analysis |

`VCHECK` |
checks standardized residuals from a `REML` analysis |

`VDEFFECTS` |
plots one- or two-way tables of effects estimated in a `REML` analysis |

`VDFIELDRESIDUALS` |
display residuals from a `REML` analysis in field layout |

`VFIXEDTESTS` |
saves fixed tests from a `REML` analysis |

`VFLC` |
performs an F-test of random effects in a linear mixed model based on linear combinations of the responses, i.e. an FLC test |

`VFPEDIGREE` |
checks and prepares pedigree information from several factors, for use by `VPEDIGREE` and `REML` |

`VFRESIDUALS` |
obtains residuals, fitted values and their standard errors from a `REML` analysis |

`VFUNCTION` |
calculates functions of variance components from a `REML` analysis |

`VGRAPH` |
plots tables of means from `REML` |

`VHERITABILITY` |
calculates generalized heritability for a random term in a `REML` analysis |

`VLSD` |
prints approximate least significant differences for `REML` means |

`VMCOMPARISON` |
performs pairwise comparisons between `REML` means |

`VMETA` |
performs a multi-treatment meta analysis using summary results from individual experiments |

`VPERMTEST` |
does random permutation tests for the fixed effects in a REML analysis |

`VPLOT` |
plots residuals from a `REML` analysis |

`VPOWER` |
uses a parametric bootstrap to estimate the power (probability of detection) for terms in a `REML` analysis |

`VRACCUMULATE` |
forms a summary accumulating the results of a sequence of `REML` random models |

`VRCHECK` |
checks effects of a random term in a `REML` analysis |

`VRMETAMODEL` |
forms the random model for a `REML` meta analysis |

`VRPERMTEST` |
performs permutation tests for random terms in `REML` analysis |

`VRFIT` |
fits terms from a `REML` fixed model in a Genstat regression |

`VRADD` |
adds terms from a `REML` fixed model into a Genstat regression |

`VRDISPLAY` |
displays output for a `REML` fixed model fitted in a Genstat regression |

`VRDROP` |
drops terms in a `REML` fixed model from a Genstat regression |

`VRKEEP` |
saves output for a `REML` fixed model fitted in a Genstat regression |

`VRSETUP` |
sets up Genstat regression to assess terms from a `REML` fixed model |

`VRSWITCH` |
adds or drops terms from a `REML` fixed model in a Genstat regression |

`VRTRY` |
tries the effect of adding and dropping individual terms from a `REML` fixed model in a Genstat regression |

`VSAMPLESIZE` |
estimates the replication to detect a fixed term or contrast in a `REML` analysis, using parametric bootstrap |

`VSCREEN` |
performs screening tests for fixed terms in a `REML` analysis |

`VSOM` |
analyses a simple `REML` variance components model for outliers using a variance shift outlier model |

`VSPREADSHEET` |
saves results from a `REML` analysis in a spreadsheet |

`VSURFACE` |
fits a 2-dimensional spline surface using `REML` , and estimates its extreme point |

`VTCOMPARISONS` |
calculates comparison contrasts within a multi-way table of predicted means from a `REML` analysis |

`VUVCOVARIANCE` |
forms the unit-by-unit variance-covariance matrix for specified variance components in a `REML` model |

There is also a suite of procedures to provide automatic selection of `REML`

random models for single trials, series of trials and meta analysis.

`VABLOCKDESIGN` |
analyses an incomplete-block design by `REML` , allowing automatic selection of random and spatial covariance models |
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`VAROWCOLUMNDESIGN` |
analyses a row-and-column design by `REML` , with automatic selection of the best random and spatial covariance model |

`VALINEBYTESTER` |
provides combinabilities and deviances for a line-by-tester trial analysed by `VABLOCKDESIGN` or `VAROWCOLUMNDESIGN` |

`VLINEBYTESTER` |
analyses a line-by-tester trial by `REML` |

`VASERIES` |
analyses a series of trials with incomplete-block or row-and-column designs by `REML` , automatically selecting the best random models |

`VASDISPLAY` |
displays further output from an analysis by `VASERIES` |

`VASKEEP` |
copies information from an analysis by `VASERIES` into Genstat data structures |

`VASMEANS` |
saves experiment × treatment means from analysis of a series of trials by `VASERIES` . |

`VAMETA` |
performs a `REML` meta analysis of a series of trials |

`VFMODEL` |
forms a model-definition structure for a `REML` analysis |

`VFSTRUCTURE` |
adds a covariance-structure definition to a `REML` model-definition structure |

`VAOPTIONS` |
defines options for the fitting of models by `VARANDOM` and associated procedures |

`VARANDOM` |
finds the best `REML` random model from a set of models defined by `VFMODEL` |

`VARECOVER` |
recovers when `REML` , is unable to fit a model, by simplifying the random model |