Calculate Oakey's heritability from model object

Compute heritability for genotype means using the variance–covariance matrix of the genotype BLUPs as described by Oakey et al. (2006).

Usage

H2_Oakey(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

Details

$$H^2_{Oakey} = \frac{\sum_{i = n_z+1}^{n_g} \lambda_i}{\sum_{n_g}^{\lambda_i\neq 0}}$$ where:

$n_g$ is the number of genotypes
$n_z$ is the number of zero eigenvalues
$\lambda_i$ is the ith eigenvalue of the matrix $I_{m} - G^{-1}C^{gg}$
$\sigma^2$ is the variance attributed to differences between genotype

See pages 813 and 818 of the reference for full derivation and explanation for Oakey's heritability

References

Oakey, H., Verbyla, A., Pitchford, W., Cullis, B., & Kuchel, H. (2006). Joint modeling of additive and non-additive genetic line effects in single field trials. Theoretical and Applied Genetics, 113(5), 809–819. https://doi.org/10.1007/s00122-006-0333-z

Examples

# lme4 model
lettuce_subset <- lettuce_phenotypes |> subset(loc == "L2")
lettuce_lme4 <- lme4::lmer(y ~ rep + (1 | gen), data = lettuce_subset)
H2_Oakey(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_Oakey(lettuce_asreml, target = "gen")
} # }