Calculate reliability from model object

Compute the reliability ($r^2$, also known as the coefficient of determination) of the genotype BLUPs, as described by Schmidt et al. (2019). h2_Reliability() / H2_Reliability() return the overall (mean) reliability $\bar{r}^2$, while h2_Reliability_by_genotype() / H2_Reliability_by_genotype() return the per-genotype values $r^2_i$.

Usage

H2_Reliability(
  model,
  target,
  options = NULL,
  marginal = TRUE,
  stratification = NULL,
  vc = NULL,
  ...
)

H2_Reliability_by_genotype(
  model,
  target,
  options = NULL,
  marginal = TRUE,
  stratification = NULL,
  vc = NULL,
  ...
)

h2_Reliability(
  model,
  target,
  options = NULL,
  marginal = TRUE,
  stratification = NULL,
  vc = NULL,
  ...
)

h2_Reliability_by_genotype(
  model,
  target,
  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.
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

h2_Reliability() / H2_Reliability() return a numeric value; h2_Reliability_by_genotype() / H2_Reliability_by_genotype() return a named numeric vector.

Details

The reliability of the $i$th genotype is $$r^2_i = 1 - \frac{var(\hat{g}^{BLUP}_i)}{var(g_i)}$$ where $var(\hat{g}^{BLUP}_i)$ is the $i$th diagonal element of the prediction error variance matrix $C_{22(g)}$ and $var(g_i)$ is the $i$th diagonal element of the genotypic variance-covariance matrix $G_{(g)}$. As only the diagonal elements are used, $r^2_i$ ignores the off-diagonal elements (covariances) of both matrices. The overall reliability is the mean across genotypes, $$\bar{r}^2 = \frac{1}{n_g}\sum_{i=1}^{n_g} r^2_i.$$

References

Schmidt, P., Hartung, J., Bennewitz, J., & Piepho, H.-P. (2019). Heritability in Plant Breeding on a Genotype-Difference Basis. Genetics, 212(4), 991–1008. https://doi.org/10.1534/genetics.119.302134
Mrode, R. A. (2014). Linear Models for the Prediction of Animal Breeding Values (3rd ed.). CABI.

Examples