REML analysis of linear mixed models

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
`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
`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
`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

Updated on January 12, 2022

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