Difference between multilevel modelling and mixed effects models?

What is the difference between Multilevel/Hierarchical Modelling and Mixed Effects Models?

Wikipedia considers them to be the same, i.e. two different names for the same thing. But I think they are not exactly the same. Could anybody explain the theoretical difference?

Maybe the “Mixed Effects Models” is just one approach to solve Multilevel problems?

Answer

Section 2.2.2.1 from lme4 book

Because each level of sample occurs with one and only one level of batch we
say that sample is nested within batch. Some presentations of mixed-effects
models, especially those related to multilevel modeling˜[Rasbash et˜al., 2000]
or hierarchical linear models˜[Raudenbush and Bryk, 2002], leave the impression
that one can only define random effects with respect to factors that
are nested. This is the origin of the terms “multilevel”, referring to multiple,
nested levels of variability, and “hierarchical”, also invoking the concept of
a hierarchy of levels. To be fair, both those references do describe the use
of models with random effects associated with non-nested factors, but such
models tend to be treated as a special case.

The blurring of mixed-effects models with the concept of multiple, hierarchical
levels of variation results in an unwarranted emphasis on “levels”
when defining a model and leads to considerable confusion. It is perfectly legitimate
to define models having random effects associated with non-nested
factors. The reasons for the emphasis on defining random effects with respect
to nested factors only are that such cases do occur frequently in practice and
that some of the computational methods for estimating the parameters in
the models can only be easily applied to nested factors

Attribution
Source : Link , Question Author : skan , Answer Author : rightskewed

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