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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, or to produce additional output from a REML analysis.

    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
    VAIC calculates the Akaike and Schwarz (Bayesian) information coefficients for REML
    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
    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
    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
    VRMETA forms the random model for a REML meta analysis
    VRPERMTEST performs permutation tests for random terms in REML analysis
    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
   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
   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 September 22, 2020

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