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This analytical problem can be avoided by modeling a nested structure of contexts where students are situated under a class.
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Location effect was controlled by modeling nest ID as a random effect.
Using this supercomputer and GPU technology, the whole calculation takes a few minutes for building the models, followed by a nested simulation time on the order of about an hour for processing a billion scenarios on a realistic banking derivative portfolio.
Multiple prediction partitioning was performed using Sarment Python modules (Guéguen 2005) to build an incremental partitioning of the sequence of replicon a when hybridized with strain i into segments of consecutive probes of common Absent or Present state given the likelihoods of each probe by models (A) and (P) nested in the optimized model (M).
Primarily overall group differences are identified by a model comparing likehood ratio test of a hypothesized model incorporating interaction effects of group by time and a nested null model leaving out these interactions.
This issue is known as prediction equivalence and is due to the fact that subset relationships, which are represented by a nested effects model, are transitive in principle.
In fact, lim n →∞ BF ij Schwarz /BF ij =1 if BF ij Schwarz is the BIC approximation of the BF and BF ij is the BF that corresponds to a nested null model defined by a single value of the parameter of interest, in this case β ij, that has a normal prior with information equal to that of one observation (Kass and Wasserman, 1995).
The use of maximum likelihood to measure model fit allows for testing of specific hypotheses by comparing a model and nested submodels using the chi-square statistic.
We evaluated different demographic models by comparing relevant nested models (L-mode) to the full six-parameter model and assessed the significance by likelihood ratio tests implemented in the software [ 33].
The fixed effects and all one-way interactions with biological meaning included in the models were initially selected step-by-step using nested models that were compared with the likelihood ratio test.
We model these explicitly, as we replace SNP alleles by haplotypes and we construct a model of nested HMMs that fully controls for LD between SNPs along the same haplotype to improve resolution of ancestry parsing.
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