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*