VGESELECT procedure

Selects the best variance-covariance model for a set of environments (M.P. Boer, M. Malosetti, S.J. Welham & J.T.N.M. Thissen).

Options

PRINT = string tokens	What to print (summary, best, model, components, effects, means, stratumvariances, monitoring, vcovariance, deviance, waldtests, missingvalues, covariancemodels); default summ, best, comp, cova
VCMODELS = string tokens	Specifies the variance-covariance models that are to be compared for the set of environments (identity, diagonal, cs, hcs, outside, fa, fa2, unstructured); default iden, diag, cs, hcs, outs, fa, fa2, unst
CRITERION = string token	Defines which criterion is used to compare the different covariance structures (aic, sic); default sic
FIXED = formula	Defines extra fixed effects
UNITFACTOR = factor	Saves the units factor required to define the random model when UNITERROR is to be used
MVINCLUDE = string tokens	Whether to include units with missing values in the explanatory factors and variates and/or the y-variates (explanatory, yvariate); default expl, yvar
MAXCYCLE = scalar	Limit on the number of iterations; default 100
WORKSPACE = scalar	Number of blocks of internal memory to be set up for use by the REML algorithm; default 100

Parameters

TRAIT = variates	Quantitative trait to be analysed; must be set
GENOTYPES = factors	Genotype factor; must be set
ENVIRONMENTS = factors	Environment factor; must be set
UNITERROR = variate	Uncertainty on trait means (derived from individual unit or plot error) to be included in QTL analysis; default * i.e. omitted
SELECTEDMODEL = texts	VCMODELS setting for the best variance-covariance model
SAVE = REML save structures	Save the details of each REML analysis for use in subsequent VDISPLAY and VKEEP directives

Description

VGESELECT selects the best covariance structure for genetic correlations between environments. The quantitative trait is specified by the TRAIT parameter, and the environment and genotype factors are specified by the ENVIRONMENTS and GENOTYPES parameters respectively. The UNITERROR parameter allows you to specify uncertainty on the trait means (derived from individual unit or plot error) to include in the random model; by default this is omitted. The UNITFACTOR option allows you to save the factor that is needed to define the unit-error term (you would need this, for example, if you later wanted to save information about the term using VKEEP).

The settings of the VCMODELS option indicate which models to consider for the variance-covariance structure (see the Method Section for details). The CRITERION option specifies whether to assess the different covariance structures by using the Bayesian Information Criterion (BIC), which is also known as the Schwarz Information Criterion (SIC), or by using Akaike’s Information Criterion (AIC). The default is to use the Schwarz (Bayesian) criterion. The SELECTEDMODEL parameter can save the setting corresponding to the best covariance structure can be saved.

The PRINT option controls the printed output. The summary setting prints a summary of the analyses, and best prints details of the best model. The other settings correspond to the settings of the PRINT option of the REML directive. The specified output is printed for each model specified by the MODELS option.

The FIXED option can be used to include extra fixed effects, e.g. selected QTLs (genetic predictors). There are also MVINCLUDE, MAXCYCLE and WORKSPACE options which operate in the same way as these options in the REML directive.

Options: PRINT, VCMODELS, CRITERION, FIXED, UNITFACTOR, MVINCLUDE, MAXCYCLE, WORKSPACE.

Parameters: TRAIT, GENOTYPES, ENVIRONMENTS, UNITERROR, SELECTEDMODEL, SAVE.

Method

The method selects the best variance-covariance matrix to model the genetic correlations between environments, based on the Schwarz (Bayesian) Information Criterion (BIC) or Akaike Information Criterion (AIC), as described by Malosetti et al. (2004) and Boer et al. (2007). The AIC and BIC are defined by:

AIC = deviance + 2 × p,

BIC (or SIC) = deviance + log(N) × p,

where N is the total number of observations, and p is the number of parameters in the variance-covariance matrix. The default is to use the Schwarz (Bayesian) criterion.

The variance-covariance models that can be specified by the VCMODELS option to be compared are as follows:

 

In this table n_env is the number of environments, σ2e and σ2g are scalars, and λ is a n_env dimensional vector. In addition, I is the n_env × n_env identity matrix, J is the n_env × n_env matrix with all values equal to one, K is the n_env × n_env matrix with one in its diagonal elements and θ in its off-diagonal elements, and D is a diagonal matrix containing the variances (σ_ei²:i = 1…n_env).

The analyses are performed by the REML directive, using the VSTRUCTURE directive to specify the covariance models. The table below summarizes how the models are specified in Genstat notation.

Action with RESTRICT

Restrictions are not allowed.

References

Boer, M.P., Wright, D,, Feng, L., Podlich, D.W., Luo, L., Cooper, M. & van Eeuwijk F.A. (2007). A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize. Genetics, 177, 1801-1813.

Malosetti, M., Voltas, J., Romagosa, I., Ullrich, S.E. & van Eeuwijk, F.A. (2004). Mixed models including environmental covariables for studying QTL by environment interaction. Euphytica, 137, 139-145.

See also

Procedures: QMVAF, QMBACKSELECT, QMESTIMATE, QMQTLSCAN.

Commands for: REML analysis of linear mixed models, Statistical genetics and QTL estimation.

Example

CAPTION    'VGESELECT example'; STYLE=meta
SPLOAD     '%GENDIR%/Examples/F2maize_traits.gsh'
VGESELECT  [PRINT=summary,best,comp,covariance;\ 
           VCMODELS=id,diag,cs,hcs,outside,fa,fa2,unstructured]\ 
           TRAIT=yld; ENVIRONMENTS=E; GENOTYPES=G; SELECTEDMODEL=Bestmodel
PRINT      Bestmodel