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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, 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
 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
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 November 24, 2020

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