Calculate the correlated response to selection (CRDR) based on the fitted
model. The CRDR is calculated as described by Atlin et al. E.g. for a model
with trials nested within scenarios, which has a random part that looks like
this: genotype + genotype:scenario + genotype:scenario:trial the CRDR is
calculated as:
$$H1 = \sigma_G^2 / (\sigma_G^2 + \sigma_S^2 / s + \sigma_{ST}^2 / st +
\sigma_E^2 / str)$$
$$H2 = (\sigma_G^2 + \sigma_S^2) / (\sigma_G^2 + \sigma_S^2 +
\sigma_{ST}^2 / st + \sigma_E^2 / str)$$
$$CRDR = (\sigma_G^2 / (\sigma_G^2 + \sigma_S^2)) * sqrt(H1 / H2)$$
In these formulas the \(\sigma\) terms stand for the standard deviations of
the respective model terms, and the lower case letters for the number of
levels for the respective model terms. So \(\sigma_S\) is the standard
deviation for the scenario term in the model and \(s\) is the number of
scenarios. \(\sigma_E\) corresponds to the residual standard deviation and
\(r\) to the number of replicates.
References
Atlin, G. N., Baker, R. J., McRae, K. B., & Lu, X. (2000). Selection response in subdivided target regions. Crop Science, 40(1), 7–13. doi:10.2135/cropsci2000.4017
See also
Other Mixed model analysis:
correlations(),
diagnostics(),
gxeVarComp(),
herit(),
plot.varComp(),
predict.varComp(),
vc()