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In between the "complete pooling" approach implicit in the averaging method and the "complete independence" approach implicit in per-participant analyses lies a compromise solution known as hierarchical modelling (Rouder & Lu, 2005; Shiffrin, Lee, Kim, & Wagenmakers, 2008).
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Thus, the relative differences between partial pooling on the one hand and no and complete pooling on the other hand increased with increasing number of markers.
Partial pooling thus strikes a middle ground between no pooling (specific marker effects estimated from data of the specific population only) and complete pooling (common marker effects estimated from pooled training sets).
We derive cost expressions for this routed pooling policy as well as for the no pooling and complete pooling policies, which serve as benchmarks.
For no pooling, the model was applied to each population in turn, for complete pooling to the joint data set.
It is therefore a compromise between no pooling, which models unique characteristics of each population but ignores shared information, and complete pooling, in which the opposite is the case.
CPU time increased linearly with the number of markers for no and complete pooling, but exponentially for partial pooling.
Averaged over traits and P and N p combinations, the difference between 285 and 575 markers were statistically not significant (p > 0.05) for r Π of no and complete pooling and for r Π ¯ of partial and complete pooling.
This pool was assayed as described above for the complete homozygous deletion pool.
In fact, the first five principal components are capable to reproduce between the 72% 100% of the complete variability along the metabolic pool libraries, see Figure 6.
The initial analysis included the complete 54 − item pool and results are presented in Table 1.
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