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?
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
