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This large difference implies that the simple arithmetic mean model is probably biased towards model C for the dipole terms.

Interestingly, the residual map for the SV candidate model A when compared to the mean model is similar in shape to the residual map that was observed between the IGRF-2015 candidate model A and the mean model (Fig. 7).

We emphasize that in the case of SV models it is much more difficult to be certain that a particular candidate is in error simply because it differs from a mean model, because there are non-random difficulties in field forecasting, and because it is not obvious that a mean model is more likely to be correct.

The mean model is suitable for analyzing datasets with more uncertain prior knowledge, which calculates the average gene expression level.

Thus, a sire-dam variance model implies that genetic heterogeneity of residual variance in the mean model is completely explained by sire and dam effects.

Given the mean model is slightly better in terms of fit and numbers of inconsistencies this is the one recommended for use.

Conversely, none of the candidate models that compared well to the arithmetic mean model are allocated full weight for all three components.

Models showing the largest variance about the mean were either rejected or down-weighted, and the arithmetic mean model was recalculated from the remaining weighted models until some kind of convergence.

In Model 2, the conditional mean model was augmented with the AR(1) term, which was found to be statistically significant along with the test for heteroscedastic ARCH effects.

The spline model also had a smaller DIC value (416.7) than the linear model, but the shape of the trend was very complex, indicating that the mean model was also the most appropriate one in this case.

Furthermore, a preliminary analysis of the real data also revealed that partitioning additive genetic and common environmental effects in the variance model was sensitive to transformation of data, while the mean model was rather robust in this regard.