Browsing by Subject "Average semivariance"

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An adjusted coefficient of determination (R2) for generalized linear mixed models in one go
(2023) Piepho, Hans‐Peter
The coefficient of determination (R2) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.
Assessing the efficiency and heritability of blocked tree breeding trials
(2024) Piepho, Hans-Peter; Williams, Emlyn; Prus, Maryna
Progeny trials in tree breeding are often laid out using blocked experimental designs, in which families are randomly assigned to plots and several trees are planted per plot. Such designs are optimized for the assessment of family effects. However, tree breeders are primarily interested in assessing breeding values of individual trees. This paper considers the assessment of heritability at both the family and tree levels. We assess heritability based on pairwise comparisons among individual trees. The approach shows that there is considerable heterogeneity in pairwise heritabilities, primarily due to the differences in both genetic as well as error variances among within- and between-family comparisons. Our results further show that efficient blocking positively affects all types of comparison except those among trees within the same plot.