Calculate average heritability of differences between genotypes from model object

Instead of computing heritability on a "entry-mean" basis, this method calculates heritability using "entry-differences". Entry here is referring to the genotype, line or variety of interest. See reference for origin and interpretation of h2/H2_Delta and it's variants

Usage

h2_Delta(model,
         target,
         type = c("BLUP", "BLUE"),
         options = NULL,
         marginal = TRUE,
         stratification = NULL,
         vc = NULL,
         ...)

H2_Delta(model,
         target,
         type = c("BLUP", "BLUE"),
         options = NULL,
         marginal = TRUE,
         stratification = NULL,
         vc = NULL,
         ...)

Arguments

model: Model object of class lmerMod/merMod or asreml
target: The name of the random effect for which heritability is to be calculated.
type: character, whether heritability is calculated using BLUEs or BLUPs
options: NULL by default, for internal checking of model object before calculations
marginal: Logical; if TRUE, construct marginal (strata-averaged) mappings so that each genotype receives a single averaged effect per term. If FALSE, mappings will only consider the main genotype effect and ignore the iteracting terms.
stratification: A one-row data frame defining the stratum in which genotype effects should be evaluated. The columns must correspond to model terms that interact with target.
vc: A list of precomputed variance components. Should be in the same structure as the output of var_comp()
...: Additional arguments that specify heritability calculation when interactions with genotype effects are modelled

Value

Numeric

Details

The broad-sense heritability of differences between genotypes is given by:

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

where:

$PEV^{BLUP}_{\overline\Delta ..}$ is the mean of the prediction error variance matrix for the pairwise differences among BLUPs (BLUEs if method = "BLUE") across all genotypes
$\sigma^2$ is the variance attributed to differences between genotype

The narrow-sense heritability of differences between genotypes is given by:

$$h^2_{\Delta ij} = 1 - \frac{PEV^{BLUP}_{\overline\Delta ij}}{\operatorname{Var}(g_i - g_j)}$$

where:

$g_i$ is the random effect of the $i^{th}$ genotype

See reference page 995 - 997 for full derivation of this heritability measure and related variants

References

Schmidt, P., Hartung, J., Rath, J., & Piepho, H.-P. (2019). Estimating Broad-Sense Heritability with Unbalanced Data from Agricultural Cultivar Trials. Crop Science, 59(2), 525–536. https://doi.org/10.2135/cropsci2018.06.0376

Examples

# lme4 model
lettuce_subset <- lettuce_phenotypes |> subset(loc == "L2")
lettuce_lme4 <- lme4::lmer(y ~ rep + (1 | gen), data = lettuce_subset)
H2_Delta(lettuce_lme4, target = "gen", type = "BLUP")
#> [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_Delta(lettuce_asreml, target = "gen", type = "BLUP")
} # }