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Let us supposed a continuous outcome distributed according to the following mixed-effects model: Y ijk = θ i + β ij + ε ijk (1) where Y ijk is the observed response for the kth subject in the jth cluster of the ith group, θ i is the overall mean in the ith group, β ij is the random effect associated with the cluster effect and ε ijk is the residual effect.
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Hence, let us suppose it true.
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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