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Thus practices 1, 2 and 19 in Table 9 have high yi (and high maximum likelihood relative risks ratios yi/Oi) even after taking account of covariate values, including high deprivation.
Bold entries indicate statistically significant rate heterogeneity by the maximum likelihood relative rate test.
The power of maximum likelihood relative rate tests was investigated by determining the degree of rate heterogeneity required to reliably reject rate constancy for DNA sequences simulated under average nucleotide substitution parameters of ITS sequences.
Overall, the simulations indicated that a maximum likelihood relative rate test had an increasing chance to detect rate heterogeneity for ITS-like sequences as the rate difference between ingroup taxa increased.
We investigated the power of maximum likelihood relative rate tests for each of the ITS1, ITS2 and combined ITS regions by computer simulation by utilizing empirically estimated sequence substitution parameters.
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The maximum-likelihood relative rate tests were implemented in HyPhy [ 60] and used the nucleotide substitution models from Modeltest.
The maximum-likelihood relative rate test rejected the null hypothesis of rate constancy in 12 out of 48 comparisons with less divergent outgroups and in 13 out of 48 comparisons with more divergent outgroups.
Results from the maximum-likelihood relative rate test and the categorical treatment of branch length differences, as well as the estimated rate differences in 16 independent annual/perennial comparisons for the ITS1, ITS2 and combined ITS data using two outgroup taxa, are summarized in Table 1.
Simulations have shown that the power of Tajima's relative rate test [ 36], distance-based relative rate tests [ 9], and the maximum-likelihood relative ratio test [ 6] are all dependent on sequence lengths, the relatedness of the outgroup taxa, and the employment of an appropriate model of nucleotide substitution [ 37, 38].
The maximum-likelihood relative rate test is considered one of the most powerful and flexible tests for rate heterogeneity, but it requires knowledge of the nucleotide substitution pattern, any substitution rate variation among sites in addition to the phylogenetic relationship among sequences [ 27].
The InVEst method estimates the parameters of kinetic rate Eq. (2) using maximum likelihood, assuming relative error in all measurements.
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