Mixed model analysis of GxE table of means

This function fits a mixed model best fitting to the data in a TD object. The exact model fitted is determined by both the structure of the genotype by environment table of observations and the chosen parameters.

Six different types of models can be fitted depending on the structure of the environments in the data. These models are described in the table below, together with the function parameters used in gxeVarComp to fit the model.

Structure of environments	Model	Function parameters
Environments correspond to trials	trait = trial + genotype + genotype:trial
Trials form a factorial structure of locations x years	trait = year + location + year:location + genotype + genotype:year + genotype:location + genotype:year:location	`locationYear = TRUE`
Trials are nested within year	trait = year + year:trial + genotype + genotype:year + genotype:year:trial	`nestingFactor = "year"`
Trials are nested within locations	trait = location + location:trial + genotype + genotype:location + genotype:location:trial	`nestingFactor = "loc"`
Trials correspond to locations within regions across years	trait = region + region:location + year + region:year + region:location:year + genotype + genotype:region + genotype:region:location + genotype:year + genotype:region:year + genotype:region:location:year	`regionLocationYear = TRUE`
Trials are nested within scenarios	trait = scenario + scenario:trial + genotype + genotype:scenario + genotype:scenario:trial	`nestingFactor = "scenario"`

In the models above the random part of the model is printed bold.
For data in the form of GxE means, the last random term in all models above will become a residual term. If the GxE means are provided together with weights, then a residual term will be added to the models above.

The function first fits a model where all model terms are included as fixed terms. Based on the ANOVA table of this model, terms in the fixed part of the model that are likely to give a problem when fitting the mixed model are removed because of the reduced connectivity and number of available observations to estimate that model term. Also a warning is printed if the mean sum of squares for a model term points to a possible zero variance component in the mixed model.

Then a model is fitted where all model terms are included as random terms. Based on the variance components in this model the percentage of variance explained by each of the model components is determined. The percentages of variance are printed in the model summary, together with the variance components. The latter are presented on a standard deviation scale.

Finally a mixed model is fitted as specified in the overview above. Based on this mixed model variance components can be computed using vc, heritabilies can be computed using herit and predictions can be made using predict.varComp. Predictions of genotypic performance can be made at the level of individual trials, or for groups of trials by using predictLevel.

Usage

gxeVarComp(
  TD,
  trials = names(TD),
  trait,
  engine = c("lme4", "asreml"),
  locationYear = FALSE,
  nestingFactor = NULL,
  regionLocationYear = FALSE,
  useWt = FALSE,
  diagnostics = FALSE
)

Arguments

TD: An object of class TD.
trials: A character string specifying the trials to be analyzed. If not supplied, all trials are used in the analysis.
trait: A character string specifying the trait to be analyzed.
engine: A character string specifying the engine used for modeling. Either "lme4" or "asreml".
locationYear: Should a model be fitted assuming a factorial structure of locations x years?
nestingFactor: A character string specifying a column in TD specifying the nesting structure of the trials.
regionLocationYear: Should a model be fitted assuming locations within regions across years?
useWt: Should the model be fitted using weights? Doing so requires a column wt in the data. If useWt = FALSE, the default, and the data contains no replicates, the last model term will be dropped and used as homogeneous residual.
diagnostics: Should diagnostics on missing combinations of model variables be printed?

Value

An object of class varComp, a list containing:

fitMod: The fitted model.
modDat: A data.frame containing the data used when fitting the model.
nestingFactor: A name of the variable used as nesting variable in the model.
useLocYear: A boolean specifying if a model containing location x year interaction was fitted.
fullRandVC: A data.frame containing the variance components for the fully random model.
aovFullMixedMod: A data.frame containing the ANOVA table for the fully fixed model.
engine: The engine used for fitting the model.
diagTabs: A list of data.frame, one for each random model term, containing the missing combinations in the data for that term.

Examples

## Fit a mixed model.
geVarComp <- gxeVarComp(TD = TDMaize, trait = "yld")

## Summarize results.
summary(geVarComp)
#> Fitted model formula final mixed model
#> 
#>  yld ~ trial + (1 | genotype) 
#> 
#> Sources of variation for fully random model:
#>  yld ~ (1 | trial) + (1 | genotype) 
#> 
#>           Component % Variance expl.
#> trial      86448.61          81.89 %
#> genotype    6670.93           6.32 %
#> residuals  12446.94          11.79 %
#> 
#> Analysis of Variance Table for fully fixed model:
#>  yld ~ trial + genotype 
#> 
#>             Df    Sum Sq  Mean Sq   F value    Pr(>F)    
#> trial        7 127771687 18253098 1466.4731 < 2.2e-16 ***
#> genotype   210  13821018    65814    5.2876 < 2.2e-16 ***
#> residuals 1470  18296997    12447                        
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

## Plot the standard deviations.
plot(geVarComp)


## Generate predictions
pred <- predict(geVarComp, predictLevel = "trial")
head(pred)
#>   genotype trial predictedValue
#> 1     G001 HN96b       529.1555
#> 2     G002 HN96b       508.8126
#> 3     G003 HN96b       500.3794
#> 4     G004 HN96b       375.9096
#> 5     G005 HN96b       495.8588
#> 6     G006 HN96b       454.9297

Usage

Arguments

Value

See also

Examples