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All that matters is that some substitution matrices result in higher model selection scores than others.
Second, model selection scores provide the evidence for each hypothesis, not just against the "null".
Hence the extremely large model selection scores strongly suggest that these approximations are reasonable, since subtle differences in background frequencies will have a negligible effect on the model selection scores reported in my Nature letter.
Model selection scores are relative to the common ancestry model; negative scores (LLR and ΔAIC) indicate better models.
The key observation is that star trees are worse than independent origin models for the real proteins (as gauged by the model selection scores).
This control was performed for the universal protein data, and the bias was found to be negligible compared to the true (unpermuted) model selection scores (hundreds of log-likelihood units versus thousands, respectively, indicating a maximum ~10% error in the reported model selection scores).
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To evaluate whether including fitting vB in the 2TCM improved the fit of the cerebellar [18F]MNI-659 model curve as compared to the 2TCM with vB estimated from the fitting of the whole brain, the sum of squared residuals, χ 2, and model selection criteria scores were calculated, and an F test was performed.
The Akaike's information criterion (AIC) was used for model selection, using differences in AIC scores (lower scores indicated greater statistical support).
From the model outputs, we defined selection scores representing the strength and frequency of positive, neutral, and negative selection across all sites in a gene.
jModelTest (version 2.1.10) package (Darriba et al. 2012) was used for substitution model selection by computing likelihood score out of 56 models.
Risk factors that met these criteria were subjected to a chi-square score model selection procedure to obtain the most significant and stable multivariate model.
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