Calculate Cullis' heritability from model object

Compute "generalised heritability" for unbalanced experimental designs. See Cullis, Smith and Coombes (2006) for derivation.

Usage

H2_Cullis(model, target, options)

Arguments

model: Model object of class lmerMod/merMod or asreml
target: The name of the random effect for which heritability is to be calculated.
options: NULL by default, for internal checking of model object before calculations

Value

Numeric value

Details

The equation for Cullis heritability is as follow

$$H^2_{Cullis} = 1 - \frac{PEV^{BLUP}_{\overline\Delta ij}}{2\sigma^2_g}$$

where:

$PEV$ is the prediction error variance matrix of the pairwise differences among BLUPS
$\sigma^2$ is the variance attributed to differences between genotype

References

Cullis, B. R., Smith, A. B., & Coombes, N. E. (2006). On the design of early generation variety trials with correlated data. Journal of Agricultural, Biological, and Environmental Statistics, 11(4), 381–393. https://doi.org/10.1198/108571106X154443

Examples

# lme4 model
lettuce_subset <- lettuce_phenotypes |> subset(loc == "L2")
lettuce_lme4 <- lme4::lmer(y ~ rep + (1 | gen), data = lettuce_subset)
H2_Cullis(lettuce_lme4, target = "gen")
#> [1] 0.8294971

# asreml model (Requires license)
if (FALSE) { # \dontrun{
lettuce_asreml <- asreml::asreml(fixed = y ~ rep,
                                 random = ~ gen,
                                 data = lettuce_subset,
                                 trace = FALSE
                                 )

H2_Cullis(lettuce_asreml, target = "gen")
} # }