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Even when the random vector has a discrete distribution, the feasible set defined by the probabilistic constraint is generally non-convex and it cannot be described by explicit functions [23].
The model may not be optimal but remains valid even when the random effects are not normally distributed.
Our studies also show that the permutation-based LRT has higher power than these existing tests and still maintains a reasonably high power even when the random effects do not follow a normal distribution.
Our studies have shown that the permutation-based LRT has higher power than the score test and the tests based on mixtures under a wide range of scenarios and it still maintains a reasonably high power even when the random effects do not follow a normal distribution.
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On the other hand, MI may still yield good estimates and standard errors even when the missing at random assumption is at fault [ 37].
Even when the non-randomness was apparently not so severe, the impingement function was able to show that impingement was significantly different from the random case.
This approach is likely to give better estimates than conventional approaches to missing data even when the missing-at-random assumption is not met [ 12].
Szemerédi's work, mainly in combinatorics (the study of arrangements of finite systems) and number theory, has shown that, as systems made up of discrete components get large ‑think about hyperlinked pages on the World Wide Web there is structure even when the system is utterly random.
Therefore, it should be possible to implement this method even when the fixed effects and random effects models fail.
Non-random sites pose particularly difficult problems because formal kinetic equations might still fit measured data even when the nucleation sites are non-random, as will be demonstrated in this study.
Moreover, one of them is always faster in searching random trees, even when the leaf node evaluation time is negligible.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com